A¯=2i¯+k¯ , B¯=i¯+j¯+k¯ and C¯=4i¯−3j¯+7k¯ then the vector R¯ satisfying the conditions R¯×B¯=C¯×B¯ and R¯.A¯=0

A−=2i−+k−, B−=i−+J−+k− C−=4i−−3J−+k− A−×B−=C−×B− & R−.A−=0 (R−−C−)×B−=0− R−−C−//B− R−−C−=±B− R−.A−−C−.A−=±B−.A− t=−C−.A−B−.A−=−(8+7)2+1=−5

A¯=2i¯+k¯ , B¯=i¯+j¯+k¯ and C¯=4i¯−3j¯+7k¯ then the vector R¯ satisfying the conditions R¯×B¯=C¯×B¯ and R¯.A¯=0

A−=2i−+k−, B−=i−+J−+k− C−=4i−−3J−+k− A−×B−=C−×B− & R−.A−=0 (R−−C−)×B−=0− R−−C−//B− R−−C−=±B− R−.A−−C−.A−=±B−.A− t=−C−.A−B−.A−=−(8+7)2+1=−5

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$\bar{A} = 2 \bar{i} + \bar{k}$ , $\bar{B} = \bar{i} + \bar{j} + \bar{k}$ and $\bar{C} = 4 \bar{i} - 3 \bar{j} + 7 \bar{k}$ then the vector $\bar{R}$ satisfying the conditions $\bar{R} \times \bar{B} = \bar{C} \times \bar{B}$ and $\bar{R} . \bar{A} = 0$

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$(- 1, - 8, 2)$

$(1, - 8, - 2)$

$(- 2, 8, 4)$

$(1, 0, - 2)$

answer is A.

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Detailed Solution

$\bar{A} = 2 \bar{i} + \bar{k}, \bar{B} = \bar{i} + \bar{J} + \bar{k} \bar{C} = 4 \bar{i} - 3 \bar{J} + \bar{k} \bar{A} \times \bar{B} = \bar{C} \times \bar{B} & \bar{R} . \bar{A} = 0 (\bar{R} - \bar{C}) \times \bar{B} = \bar{0} \bar{R} - \bar{C} / / \bar{B} \bar{R} - \bar{C} = \pm \bar{B} \bar{R} . \bar{A} - \bar{C} . \bar{A} = \pm \bar{B} . \bar{A} t = \frac{- \bar{C} . \bar{A}}{\bar{B} . \bar{A}} = \frac{- (8 + 7)}{2 + 1} = - 5$