The angle between the lines $\bar{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}-2 \hat{i}+\hat{k})$.…

The angle between the lines $\bar{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}-2 \hat{i}+\hat{k})$. and $\bar{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2\hat{k})$
  1. $90^{\circ}$
  2. $0^{\circ}$
  3. $30^{\circ}$
  4. $60^{\circ}$

Solution

$\theta=\cos ^{-1}\left(\frac{2 \times 1-2 \times 2+1 \times 2}{\sqrt{2^2+2^2+1^2} \sqrt{1^2+2^2+2^2}}\right)=\cos ^{-1}(0)=90^{\circ}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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