MCQ
જો $\vec a = \hat i - \hat j - \hat k$ અને $\vec b = \lambda \hat i - 3\hat j + \hat k$ અને $\vec b$ નો $\vec a$ પરનો લંબ પ્રક્ષેપ $\frac{4}{3}\left( {\hat i - \hat j - \hat k} \right)$ હોય તો $\lambda$ ની કિમત મેળવો
- A$0$
- ✓$2$
- C$12$
- D$-1$
$ \Rightarrow \frac{{\{ (\lambda \widehat i - 3\widehat j + \widehat k) \cdot (\widehat i - \widehat j - \widehat k)\} (\widehat i - \widehat j - \widehat k)}}{{(1 + 1 + 1)}}$
$=\frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$
$\Rightarrow(\lambda+3-1)(\hat{i}-\hat{j}-\hat{k})=4(\hat{i}-\hat{j}-\hat{k})$
$\Rightarrow(\lambda+2)(\hat{i}-\hat{j}-\hat{k})=4(\hat{i}-\hat{j}-\hat{k})$
On equating the coefficient of $\widehat i$, we get
$\lambda+2=4 \Rightarrow \lambda=2$
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