The direction cosines of the vector joining the points A(1, 2, −3) and B(−1, −2, 1) directed from A to B are: A. −2/6, −4/6, 4/6 B. −1/3, −2/3, 2/3 C. −2, −4, 4 D. 1/3, 2/3, −2/3 Answer: B) −1/3, −2/3, 2/3 Explanation: Vector AB = (−1−1)î + (−2−2)ĵ + (1−(−3))k̂ = −2î − 4ĵ + 4k̂. Magnitude = √((−2)² + (−4)² + 4²) = √36 = 6. Direction cosines are −2/6, −4/6, 4/6, which simplify to −1/3, −2/3, 2/3.

imo class 12 vector algebra

The direction cosines of the vector joining the points A(1, 2, −3) and B(−1, −2, 1) directed from A to B are:

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The direction cosines of the vector joining the points A(1, 2, −3) and B(−1, −2, 1) directed from A to B are:

A. −2/6, −4/6, 4/6
B. −1/3, −2/3, 2/3
C. −2, −4, 4
D. 1/3, 2/3, −2/3

Answer: B) −1/3, −2/3, 2/3

Explanation: Vector AB = (−1−1)î + (−2−2)ĵ + (1−(−3))k̂ = −2î − 4ĵ + 4k̂. Magnitude = √((−2)² + (−4)² + 4²) = √36 = 6. Direction cosines are −2/6, −4/6, 4/6, which simplify to −1/3, −2/3, 2/3.

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