Convert the Cartesian equation x/2 = (y−1)/3 = (z+2)/−1 into a vector equation. A. r = (j − 2k) + λ(2i + 3j − k) B. r = (2i + 3j − k) + λ(j − 2k) C. r = (i − 2k) + λ(2i + 3j + k) D. r = (−j + 2k) + λ(2i + 3j − k) Answer: A) r = (j − 2k) + λ(2i + 3j − k) Explanation: The point is (0, 1, −2) which is j − 2k. The parallel vector is 2i + 3j − k. So, r = (j − 2k) + λ(2i + 3j − k).

imo class 12 three dimensional geometry

Convert the Cartesian equation x/2 = (y−1)/3 = (z+2)/−1 into a vector equation.

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Convert the Cartesian equation x/2 = (y−1)/3 = (z+2)/−1 into a vector equation.

Answer: A) r = (j − 2k) + λ(2i + 3j − k)

Explanation: The point is (0, 1, −2) which is j − 2k. The parallel vector is 2i + 3j − k. So, r = (j − 2k) + λ(2i + 3j − k).