Q. If two lines intersect at a point, what is the sum of the angles formed at that point?
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
Show solution
Solution
When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, but the angles formed by the intersecting lines sum up to 180 degrees.
Correct Answer:
B
— 180 degrees
Learn More →
Q. If two lines intersect, what is the sum of the angles formed at the intersection? (2021)
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
Show solution
Solution
When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.
Correct Answer:
B
— 180 degrees
Learn More →
Q. If two parallel lines are cut by a transversal, and one of the alternate interior angles is 45 degrees, what is the measure of the other alternate interior angle? (2020)
A.
45 degrees
B.
135 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other angle is also 45 degrees.
Correct Answer:
A
— 45 degrees
Learn More →
Q. If two parallel lines are cut by a transversal, and one of the alternate interior angles is 75 degrees, what is the measure of the other alternate interior angle? (2020)
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate interior angle is also 75 degrees.
Correct Answer:
A
— 75 degrees
Learn More →
Q. If two parallel lines are cut by a transversal, what is the relationship between the alternate interior angles? (2020)
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unequal
Show solution
Solution
When two parallel lines are cut by a transversal, the alternate interior angles are equal.
Correct Answer:
A
— They are equal
Learn More →
Q. If vector A = 2i + 3j + k and vector B = i - 2j + 4k, what is the cross product A × B?
A.
-10i + 5j + 7k
B.
10i - 5j - 7k
C.
10i + 5j + 7k
D.
-10i - 5j + 7k
Show solution
Solution
A × B = |i j k|\n|2 3 1|\n|1 -2 4| = (3*4 - 1*(-2))i - (2*4 - 1*1)j + (2*(-2) - 3*1)k = 10i - 5j - 7k.
Correct Answer:
A
— -10i + 5j + 7k
Learn More →
Q. If vector A = 2i + 3j and vector B = -i + 4j, what is the resultant vector R = A + B?
A.
i + 7j
B.
i + j
C.
3i + 7j
D.
3i + 4j
Show solution
Solution
R = A + B = (2 - 1)i + (3 + 4)j = 1i + 7j.
Correct Answer:
A
— i + 7j
Learn More →
Q. If vector A = 2i + 3j and vector B = 3i + 4j, what is the angle between them? (2023)
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.6, θ = 53.13 degrees.
Correct Answer:
D
— 60 degrees
Learn More →
Q. If vector A = 2i + 3j and vector B = 4i + 5j, what is the angle between A and B? (2023)
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (8 + 15) / (√(13) * √(41)). θ = 60 degrees.
Correct Answer:
D
— 60 degrees
Learn More →
Q. If vector A = 2i + 3j and vector B = 4i + 5j, what is the angle between them?
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (2*4 + 3*5) / (√(2^2 + 3^2) * √(4^2 + 5^2)) = 0.5, θ = 60 degrees.
Correct Answer:
D
— 60 degrees
Learn More →
Q. If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if scaled
Show solution
Solution
Vectors A and B are parallel because B = 2A.
Correct Answer:
A
— Yes
Learn More →
Q. If vector A = 2i + 3j and vector B = 4i + k, what is the angle between A and B?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 8 + 0 + 3(0) = 8; |A| = √(2^2 + 3^2) = √13; |B| = √(4^2 + 1^2) = √17. θ = cos^(-1)(8/(√13 * √17)).
Correct Answer:
B
— 60 degrees
Learn More →
Q. If vector A = 3i + 4j and vector B = 2i - j, what is the dot product A · B?
Show solution
Solution
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
Correct Answer:
A
— 10
Learn More →
Q. If vector A = 3i + 4j and vector B = 4i + 3j, what is the cross product A × B?
Show solution
Solution
A × B = |i j k| |3 4 0| |4 3 0| = (0 - 0)i - (0 - 0)j + (9 - 12)k = -3k.
Correct Answer:
B
— 1k
Learn More →
Q. If vector A = 4i + 3j and vector B = -3i + 4j, what is the angle between them?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (4*-3 + 3*4) / (5*5) = 0, θ = 90 degrees.
Correct Answer:
A
— 90 degrees
Learn More →
Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)
A.
3i + 5j
B.
5i + j
C.
3i + j
D.
5i + 5j
Show solution
Solution
A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.
Correct Answer:
A
— 3i + 5j
Learn More →
Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector R = A + B? (2019)
A.
3i + 5j
B.
5i + j
C.
3i + j
D.
5i + 5j
Show solution
Solution
R = A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.
Correct Answer:
A
— 3i + 5j
Learn More →
Q. If vector A = 4i + 3j and vector B = 3i + 4j, what is the angle between A and B?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
135 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (12 + 12) / (5 * 5) = 24/25, θ = cos^(-1)(24/25) ≈ 60 degrees.
Correct Answer:
B
— 60 degrees
Learn More →
Q. If vector A = 4i + 3j and vector B = 4i - 3j, what is the angle between A and B? (2019)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
A · B = 16 - 9 = 7. |A| = 5, |B| = 5. cos(θ) = 7/(5*5) = 0.28, θ = 180 degrees.
Correct Answer:
C
— 180 degrees
Learn More →
Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the angle between them?
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
A · B = (5)(-5) + (12)(12) = -25 + 144 = 119. Since A and B are in opposite directions, the angle is 180 degrees.
Correct Answer:
C
— 180 degrees
Learn More →
Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the resultant vector A + B? (2021)
A.
0i + 24j
B.
10i + 0j
C.
0i + 12j
D.
5i + 12j
Show solution
Solution
A + B = (5 - 5)i + (12 + 12)j = 0i + 24j.
Correct Answer:
A
— 0i + 24j
Learn More →
Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the angle between A and B?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (5*12 + 12*(-5)) / (√(169) * √(169)) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the value of A × B?
Show solution
Solution
A × B = |i j k| |5 12 0| |12 -5 0| = (0 - 0)i - (0 - 0)j + (5*-5 - 12*12)k = -85k.
Correct Answer:
A
— -85
Learn More →
Q. If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and B?
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
A · B = 5*5 + 12*(-12) = 25 - 144 = -119. Since A · B < 0, angle is 180 degrees.
Correct Answer:
C
— 180 degrees
Learn More →
Q. If vector A = 5i + 5j and vector B = 5i - 5j, what is the angle between A and B?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (25 - 25) / (√(50) * √(50)) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. If vector A = 5i + 5j and vector B = 5i - 5j, what is the angle between them?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
135 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (25 - 25) / (5√2 * 5√2) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. If vector A = 6i + 8j, what is the unit vector in the direction of A? (2023)
A.
3/5 i + 4/5 j
B.
6/10 i + 8/10 j
C.
1/5 i + 2/5 j
D.
2/5 i + 3/5 j
Show solution
Solution
Magnitude |A| = √(6^2 + 8^2) = 10. Unit vector = (1/10)(6i + 8j) = (3/5)i + (4/5)j.
Correct Answer:
A
— 3/5 i + 4/5 j
Learn More →
Q. If vector G = 4i - 3j + 2k, what is the y-component of G?
Show solution
Solution
The y-component of G is -3.
Correct Answer:
B
— -3
Learn More →
Q. If vector J = 5i + 12j, what is the angle between J and the positive x-axis?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
tan(θ) = 12/5; θ = tan^(-1)(12/5) which is approximately 67.38 degrees, closest to 60 degrees.
Correct Answer:
C
— 60 degrees
Learn More →
Q. If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L?
A.
i + 5j
B.
i + j
C.
3i + 5j
D.
3i + j
Show solution
Solution
K + L = (2i + 2j) + (-i + 3j) = (2 - 1)i + (2 + 3)j = 1i + 5j = i + 5j.
Correct Answer:
A
— i + 5j
Learn More →
Showing 811 to 840 of 1593 (54 Pages)
