If a¯=2i¯+k¯,b¯=i¯+j¯+k¯,c¯=4i¯−3j¯+7k¯ then the vector r¯ satisfying r¯×b¯=c¯×b¯ and r¯.a¯=0 is

r¯×b¯=c¯×b¯r¯−c¯×b¯=0r¯−c¯=tb¯r¯=c¯+tb¯Given r¯.a¯=0⇒r¯.a¯=c¯.a¯+tb¯.a¯0=15+t3t=−5r¯=c¯−5b¯=−i¯−8j¯+2k¯

If a¯=2i¯+k¯,b¯=i¯+j¯+k¯,c¯=4i¯−3j¯+7k¯ then the vector r¯ satisfying r¯×b¯=c¯×b¯ and r¯.a¯=0 is

r¯×b¯=c¯×b¯r¯−c¯×b¯=0r¯−c¯=tb¯r¯=c¯+tb¯Given r¯.a¯=0⇒r¯.a¯=c¯.a¯+tb¯.a¯0=15+t3t=−5r¯=c¯−5b¯=−i¯−8j¯+2k¯

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If $\bar{a} = 2 \bar{i} + \bar{k}, \bar{b} = \bar{i} + \bar{j} + \bar{k}, \bar{c} = 4 \bar{i} - 3 \bar{j} + 7 \bar{k}$ then the vector $\bar{r}$ satisfying $\bar{r} \times \bar{b} = \bar{c} \times \bar{b}$ and $\bar{r} . \bar{a} = 0$ is

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$\bar{i} + 8 \bar{j} + 2 \bar{k}$

$\bar{i} - 8 \bar{j} + 2 \bar{k}$

$\bar{i} - 8 \bar{j} - 2 \bar{k}$

$- \bar{i} - 8 \bar{j} + 2 \bar{k}$

answer is D.

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$\bar{r} \times \bar{b} = \bar{c} \times \bar{b}$

$(\bar{r} - \bar{c}) \times \bar{b} = 0$

$\bar{r} - \bar{c} = t \bar{b}$

$\bar{r} = \bar{c} + t \bar{b}$

Given $\bar{r} . \bar{a} = 0$

$\Rightarrow \bar{r} . \bar{a} = \bar{c} . \bar{a} + t \bar{b} . \bar{a}$

$0 = 15 + t (3)$

$t = - 5$

$\bar{r} = \bar{c} - 5 \bar{b} = - \bar{i} - 8 \bar{j} + 2 \bar{k}$

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If a¯=2i¯+k¯,b¯=i¯+j¯+k¯,c¯=4i¯−3j¯+7k¯ then the vector r¯ satisfying r¯×b¯=c¯×b¯ and r¯.a¯=0 is

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If $\bar{a} = 2 \bar{i} + \bar{k}, \bar{b} = \bar{i} + \bar{j} + \bar{k}, \bar{c} = 4 \bar{i} - 3 \bar{j} + 7 \bar{k}$ then the vector $\bar{r}$ satisfying $\bar{r} \times \bar{b} = \bar{c} \times \bar{b}$ and $\bar{r} . \bar{a} = 0$ is