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Question

The value of x such that the vectors $$\displaystyle a=2\hat i-\hat j+\hat k,b=x\hat i+2\hat j-3\hat k$$ and $$\displaystyle c=3\hat i-4\hat j+5\hat k$$ are coplanar is


A
1
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B
3
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C
-2
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D
0
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Solution

The correct option is A 1
$$\displaystyle a=2\hat i-\hat j+\hat k,b=x\hat i+2\hat j-3\hat k$$ and $$\displaystyle c=3\hat i-4\hat j+5\hat k$$ are coplanar

$$\Rightarrow \begin{vmatrix} 2 & -1 & 1 \\ x & 2 & -3 \\ 3 & -4 & 5 \end{vmatrix}=0$$

$$\Rightarrow -4+5x+9-4x-6=0$$

$$\therefore x=1$$

Hence, option A.

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