Question

The value of n so that vectors $2\hat{i}+3\hat{j}-2\hat{k},5\hat{i}+n\hat{j}+\hat{k}\text{and}-\hat{i}+2\hat{j}+3\hat{k}$ may be coplanar find the value ?

• A. 18
• B. 28
• C. 9
• D. 36

Answer 1

The correct option is A 18

Given $\overrightarrow{a}=2\hat{i}+3\hat{j}-2\hat{k}$

$\overrightarrow{b}=5\hat{i}+n\hat{j}+\hat{k}$ and

$\overrightarrow{c}=\widehat{-i}+2\hat{j}+3\hat{k}$

For the vectors to be co planar

$|\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}|=0$

$|\begin{array}{ccc}2& 3& -2\\ 5& n& 1\\ -1& 2& 3\end{array}|=0$

$2(3n-2)-3\left[5\right(3)+1]-2\left[5\right(2)-n]=0$

$6n-4-48-20-2n=0$

$n=\frac{72}{4}=18$

So, the correct answer is '18'.