Answer the following (internal choice): a

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Answer the following (internal choice): a. Verify that lines given by r⃗=(1−λ)i^+(λ−2)j^+(3−2λ)k^\vec{r} = (1 - \lambda)\hat{i} + (\lambda - 2)\hat{j} + (3 - 2\lambda)\hat{k} and r⃗=(μ+1)i^+(2μ−1)j^−(2μ+1)k^\vec{r} = (\mu + 1)\hat{i} + (2\mu - 1)\hat{j} - (2\mu + 1)\hat{k} are skew lines. Hence, find shortest distance between the lines. b. During a cricket match, the position of the bowler, the wicket keeper and the leg slip fielder are in a line given by B⃗=2i^+8j^\vec{B} = 2\hat{i} + 8\hat{j} , W⃗=6i^+12j^\vec{W} = 6\hat{i} + 12\hat{j} and F⃗=12i^+18j^\vec{F} = 12\hat{i} + 18\hat{j} respectively. Calculate the ratio in which the wicketkeeper divides the line segment joining the bowler and the leg slip fielder.

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