The angle between the lines r=(i+2 j+3 k)+λ(2 i-2 i+k) . and r=(i+2 j+3 k)+λ(2 i+2 i+k) i+2 j+k

Correct answer: (A) 90^°. θ=cos^-1 ((2 × 1-2 × 2+1 × 2)/(√(2^2+2^2+1^2) √(1^2+2^2+2^2)) )=cos^-1(0)=90^°

Q70 / 150 · MHT CET 2022 (07 Aug Shift 2) · Mathematics

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 $\bar{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+2 \hat{i}+\hat{k}) \hat{i}+2 j+k$

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

Hence, the correct answer is option: 'A'.