Skip to content
doubtly

The angle between the lines \(\bar{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k})\) and \(\bar{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \mu(\hat{i} + 2\hat{j} + 2\hat{k})\) is _____

Q.1 (iv) The angle between the lines \(\bar{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k})\) and \(\bar{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \mu(\hat{i} + 2\hat{j} + 2\hat{k})\) is _____

A. \(\frac{\pi}{4}\)

B. \(\frac{\pi}{2}\)

C. \(\frac{\pi}{3}\)

D. 0

1 answer

Best answer

Answer: B. \(\frac{\pi}{2}\)

Answer: (b) \(\frac{\pi}{2}\)

The direction vectors are \(\bar{b}_1 = 2\hat{i} - 2\hat{j} + \hat{k}\) and \(\bar{b}_2 = \hat{i} + 2\hat{j} + 2\hat{k}\). \(\bar{b}_1 \cdot \bar{b}_2 = 2 - 4 + 2 = 0\), so \(\cos\theta = 0\) and \(\theta = \frac{\pi}{2}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report
Was this answer helpful?

Your answer

Log in or create a free account to answer this question.