Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?
-
A.
(-3, -3, -3)
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B.
(3, 3, 3)
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C.
(5, 7, 9)
-
D.
(0, 0, 0)
Solution
A - B = (1-4, 2-5, 3-6) = (-3, -3, -3).
Correct Answer: A — (-3, -3, -3)
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Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?
Solution
A . (B × A) = 0, since B × A = 0.
Correct Answer: A — 0
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Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?
-
A.
(-5, -10, 14)
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B.
(5, 10, -14)
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C.
(10, 14, 5)
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D.
(14, -5, 10)
Solution
A × B = |i j k|\n|3 -2 1|\n|1 4 -3| = (-5, -10, 14).
Correct Answer: A — (-5, -10, 14)
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Q. If vectors A = (x, 2, 3) and B = (1, y, 4) are perpendicular, what is the value of x + y?
Solution
A · B = x*1 + 2*y + 3*4 = 0. Thus, x + 2y + 12 = 0. Solving gives x + y = -6.
Correct Answer: B — 2
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Q. If vectors A = 3i + 4j and B = 2i - j, what is the scalar product A · B?
Solution
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
Correct Answer: C — 10
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Q. If x + 2y = 10 and 2x - y = 3, what is the value of x?
Solution
From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.
Correct Answer: C — 3
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Q. If x = cos^(-1)(-1/2), what is the value of x?
-
A.
π/3
-
B.
2π/3
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C.
π/4
-
D.
π/6
Solution
x = cos^(-1)(-1/2) = 2π/3
Correct Answer: B — 2π/3
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Q. If x = cos^(-1)(1/2), then the value of sin(x) is:
Solution
If x = cos^(-1)(1/2), then x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.
Correct Answer: B — √3/2
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Q. If x = cos^(-1)(1/2), then what is the value of sin(x)?
Solution
If x = cos^(-1)(1/2), then cos(x) = 1/2, which corresponds to x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.
Correct Answer: B — √3/2
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Q. If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?
-
A.
π/3
-
B.
π/6
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C.
π/4
-
D.
0
Solution
Since x = cos^(-1)(1/2) = π/3, then sin^(-1)(1/2) = π/6.
Correct Answer: B — π/6
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Q. If x = cos^(-1)(1/2), then what is the value of sin^(-1)(√(1 - (1/2)^2))?
-
A.
π/3
-
B.
π/4
-
C.
π/2
-
D.
0
Solution
Since cos^(-1)(1/2) = π/3, we have sin^(-1)(√(1 - (1/2)^2)) = sin^(-1)(√(3/4)) = π/3.
Correct Answer: A — π/3
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Q. If x = cos^(-1)(1/2), then what is the value of x?
-
A.
π/3
-
B.
π/4
-
C.
π/2
-
D.
0
Solution
cos^(-1)(1/2) = π/3.
Correct Answer: A — π/3
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Q. If x = cos^(-1)(1/2), what is sin(x)?
Solution
If x = cos^(-1)(1/2), then x = π/3, thus sin(x) = sin(π/3) = √3/2.
Correct Answer: A — √3/2
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Q. If x = cos^(-1)(1/2), what is the value of sin(x)?
Solution
Using the identity sin(x) = sqrt(1 - cos^2(x)), we have sin(x) = sqrt(1 - (1/2)^2) = √3/2.
Correct Answer: A — √3/2
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Q. If x = sin^(-1)(-1), then the value of x is:
Solution
sin^(-1)(-1) corresponds to the angle -π/2.
Correct Answer: A — -π/2
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Q. If x = sin^(-1)(-1), what is the value of x?
Solution
sin^(-1)(-1) corresponds to the angle -π/2.
Correct Answer: A — -π/2
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Q. If x = sin^(-1)(-1/2), then what is the value of x?
-
A.
-π/6
-
B.
π/6
-
C.
-π/3
-
D.
π/3
Solution
sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.
Correct Answer: A — -π/6
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Q. If x = sin^(-1)(-1/2), what is the value of x?
-
A.
-π/6
-
B.
π/6
-
C.
π/4
-
D.
0
Solution
sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.
Correct Answer: A — -π/6
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Q. If x = sin^(-1)(1/2), then the value of cos(x) is:
Solution
If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.
Correct Answer: B — √3/2
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Q. If x = sin^(-1)(1/2), what is the value of cos(x)?
Solution
If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.
Correct Answer: B — √3/2
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Q. If x = sin^(-1)(1/3), then what is the value of cos(x)?
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A.
√(8)/3
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B.
√(2)/3
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C.
1/3
-
D.
2/3
Solution
Using the identity cos(x) = √(1 - sin^2(x)), we find cos(sin^(-1)(1/3)) = √(1 - (1/3)^2) = √(8)/3.
Correct Answer: A — √(8)/3
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Q. If x = sin^(-1)(1/3), then what is the value of cos^(-1)(√(1 - (1/3)^2))?
-
A.
π/3
-
B.
π/2
-
C.
2π/3
-
D.
π/4
Solution
Using the identity cos^(-1)(√(1 - sin^2(x))) = π/2 - x, we find that cos^(-1)(√(1 - (1/3)^2)) = π/2 - sin^(-1)(1/3).
Correct Answer: B — π/2
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Q. If x = sin^(-1)(1/√2), then what is the value of cos(x)?
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A.
1/2
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B.
√2/2
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C.
√3/2
-
D.
1
Solution
If x = sin^(-1)(1/√2), then sin(x) = 1/√2. Therefore, cos(x) = √(1 - sin^2(x)) = √(1 - (1/√2)^2) = √(1/2) = √2/2.
Correct Answer: B — √2/2
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Q. If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?
-
A.
π/4
-
B.
π/3
-
C.
π/2
-
D.
π/6
Solution
Since x = sin^(-1)(1/√2) = π/4, then cos^(-1)(x) = π/2 - π/4 = π/4.
Correct Answer: A — π/4
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Q. If x = sin^(-1)(3/5), what is cos(x)?
-
A.
4/5
-
B.
3/5
-
C.
5/4
-
D.
1/5
Solution
Using the identity cos^2(x) + sin^2(x) = 1, we find cos(x) = √(1 - (3/5)^2) = 4/5.
Correct Answer: A — 4/5
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Q. If x = sin^(-1)(3/5), what is the value of cos(x)?
-
A.
4/5
-
B.
3/5
-
C.
2/5
-
D.
1/5
Solution
Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.
Correct Answer: A — 4/5
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Q. If x = tan^(-1)(1), then the value of x is:
Solution
tan^(-1)(1) = π/4.
Correct Answer: A — π/4
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Q. If x = tan^(-1)(1), what is the value of x?
-
A.
π/4
-
B.
π/3
-
C.
π/6
-
D.
0
Solution
tan^(-1)(1) = π/4, since tan(π/4) = 1.
Correct Answer: A — π/4
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Q. If x = tan^(-1)(1/√3), what is the value of x?
-
A.
π/6
-
B.
π/4
-
C.
π/3
-
D.
0
Solution
tan^(-1)(1/√3) = π/6, since tan(π/6) = 1/√3.
Correct Answer: A — π/6
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Q. If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?
-
A.
π/3
-
B.
π/4
-
C.
π/2
-
D.
π/6
Solution
x = tan^(-1)(√3) = π/3, thus sin^(-1)(x) = sin^(-1)(√3/2) = π/3.
Correct Answer: A — π/3
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