Find the vector equation of a line passing through the point (3, 4, 5) and is parallel to the vector $2 \hat{i} + 2 \hat{j} - 3 \hat{k} .$

Open in App

Solution

Vector equation of a line passing through (3, 4, 5) and parallel to vector $\vec{a} = 2 \hat{i} + 2 \hat{j} - 3 \hat{k}$ has directions ratios (2, 2, −3)
Hence, equation of line is $\vec{r} = (3 \hat{i} + 4 \hat{j} + 5 \hat{k}) + λ (2 \hat{i} + 2 \hat{j} - 3 \hat{k})$

Suggest Corrections

Similar questions

2 i + 3 j + k

4 i - 2 j + 3 k

\hat{i} - 2 \hat{j} - 3 \hat{k}

\hat{i} - \hat{j} + 4 \hat{k} and 2 \hat{i} + \hat{j} + 2 \hat{k} .

2 \hat{i} - \hat{j} + \hat{k}

4 \hat{i} + 2 \hat{j} - 3 \hat{k} .

¯ i + 2 ¯ j + 3 ¯ ¯ ¯ k

¯ i + ¯ j + ¯ ¯ ¯ k

2 ¯ i - ¯ j + ¯ ¯ ¯ k

B

i + 2 j + 3 k

A

4 i + 2 j + 2 k

2 i + 3 j + 6 k

Join BYJU'S Learning Program