If a¯=2i¯+k¯, b¯=i¯+j¯+k¯ and c¯=4i¯−3j¯+7k¯. If d×b=c×b and d.a=0, then d will be

ijkxyz111=ijk4−37111dd×b=c×b giveswhere d=xi+yj+zksayOn solving, x=−1,y=−8,z=2Hence d=−i−8j+2k

If a¯=2i¯+k¯, b¯=i¯+j¯+k¯ and c¯=4i¯−3j¯+7k¯. If d×b=c×b and d.a=0, then d will be

ijkxyz111=ijk4−37111dd×b=c×b giveswhere d=xi+yj+zksayOn solving, x=−1,y=−8,z=2Hence d=−i−8j+2k

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If $\bar{a} = 2 \bar{i} + \bar{k}, \bar{b} = \bar{i} + \bar{j} + \bar{k}$ and $\bar{c} = 4 \bar{i} - 3 \bar{j} + 7 \bar{k}$ . If $d \times b = c \times b$ and $d . a = 0$ , then $d$ will be

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

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

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

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

answer is D.

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$|\begin{matrix} i & j & k \\ x & y & z \\ 1 & 1 & 1 \end{matrix}| = |\begin{matrix} i & j & k \\ 4 & - 3 & 7 \\ 1 & 1 & 1 \end{matrix}|$

$(d) d \times b = c \times b g i v e s$

$w h e r e d = x i + y j + z k (s a y)$

On solving, $x = - 1, y = - 8, z = 2$

Hence $d = - i - 8 j + 2 k$

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If a¯=2i¯+k¯, b¯=i¯+j¯+k¯ and c¯=4i¯−3j¯+7k¯. If d×b=c×b and d.a=0, then d will be

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If $\bar{a} = 2 \bar{i} + \bar{k}, \bar{b} = \bar{i} + \bar{j} + \bar{k}$ and $\bar{c} = 4 \bar{i} - 3 \bar{j} + 7 \bar{k}$ . If $d \times b = c \times b$ and $d . a = 0$ , then $d$ will be