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
B
3
C
-2
D
0

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.Maths

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