Q. Calculate the vector product of A = (3, 2, 1) and B = (1, 0, 2).
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A.
(4, 5, -2)
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B.
(2, 5, -3)
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C.
(2, -5, 3)
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D.
(5, -2, 3)
Solution
A × B = |i j k|\n|3 2 1|\n|1 0 2| = (4, 5, -2)
Correct Answer: A — (4, 5, -2)
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Q. Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9) using the vector product.
Solution
Area = 0.5 * |AB × AC| = 0, as points are collinear.
Correct Answer: A — 0
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Q. Find the scalar triple product of vectors A = (1, 2, 3), B = (4, 5, 6), and C = (7, 8, 9).
Solution
Scalar triple product = A · (B × C) = 0, as vectors are coplanar.
Correct Answer: A — 0
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Q. Given vectors A = (2, -1, 3) and B = (4, 0, -2), find A × B.
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A.
(-1, -10, 4)
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B.
(1, 10, -4)
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C.
(10, -1, 4)
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D.
(10, 1, -4)
Solution
A × B = |i j k|\n|2 -1 3|\n|4 0 -2| = (-1, -10, 4)
Correct Answer: A — (-1, -10, 4)
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Q. If A = (1, 0, 0) and B = (0, 1, 0), what is the vector product A × B?
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A.
(0, 0, 1)
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B.
(1, 0, 0)
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C.
(0, 1, 0)
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D.
(0, 0, 0)
Solution
A × B = (0, 0, 1) using the right-hand rule.
Correct Answer: A — (0, 0, 1)
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Q. If A = (1, 1, 1) and B = (2, 2, 2), what is A × B?
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A.
(0, 0, 0)
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B.
(1, 1, 1)
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C.
(2, 2, 2)
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D.
(3, 3, 3)
Solution
A × B = (0, 0, 0) since A and B are parallel.
Correct Answer: A — (0, 0, 0)
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Q. If A = (1, 2, 3) and B = (0, 1, 0), what is the direction of the vector product A × B?
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A.
(2, -3, 1)
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B.
(3, 0, -1)
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C.
(1, 0, -1)
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D.
(1, 3, 0)
Solution
A × B = (2, -3, 1) gives direction (2, -3, 1).
Correct Answer: B — (3, 0, -1)
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Q. If A = (1, 2, 3) and B = (4, 5, 6), what is the magnitude of the vector product A × B?
Solution
Magnitude |A × B| = √(1^2 + 2^2 + 3^2) = √14.
Correct Answer: D — √14
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Q. If A = (2, 3, 4) and B = (1, 0, -1), find the vector product A × B.
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A.
(3, 6, -3)
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B.
(3, 4, -3)
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C.
(3, -4, 6)
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D.
(3, -6, 4)
Solution
A × B = |i j k|\n|2 3 4|\n|1 0 -1| = (3, 6, -3)
Correct Answer: A — (3, 6, -3)
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