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Question: The vector equation of a line passing through (2, –1, 1) and parallel to the line whose equation is ...

The vector equation of a line passing through (2, –1, 1) and parallel to the line whose equation is x−32=y+17=z−2−3\frac{x - 3}{2} = \frac{y + 1}{7} = \frac{z - 2}{- 3}is –

A

r→=(2i^+7j^−3k^)+λ(4i^+2j^+2k^)\overrightarrow{r} = (2\widehat{i} + 7\widehat{j} - 3\widehat{k}) + \lambda(4\widehat{i} + 2\widehat{j} + 2\widehat{k})

B

r→=(2i^+7j^−3k^)+λ(2i^−j^+k^)\overrightarrow{r} = (2\widehat{i} + 7\widehat{j} - 3\widehat{k}) + \lambda(2\widehat{i} - \widehat{j} + \widehat{k})

C

r→=(2i^−j^+k^)+λ(2i^+7j^−3k^)\overrightarrow{r} = (2\widehat{i} - \widehat{j} + \widehat{k}) + \lambda(2\widehat{i} + 7\widehat{j} - 3\widehat{k})

D

None of these

Answer

r→=(2i^−j^+k^)+λ(2i^+7j^−3k^)\overrightarrow{r} = (2\widehat{i} - \widehat{j} + \widehat{k}) + \lambda(2\widehat{i} + 7\widehat{j} - 3\widehat{k})

Explanation

Solution

a→=2i^−j^+k^\overrightarrow{a} = 2\widehat{i} - \widehat{j} + \widehat{k} , b→=2i^+7j^−3k^\overrightarrow{b} = 2\widehat{i} + 7\widehat{j} - 3\widehat{k} apply, r→=a→+λb→\overrightarrow{r} = \overrightarrow{a} + \lambda\overrightarrow{b}