Find the equation of the line passing through the point (2, −1, 3) and parallel to the line $\vec{r} = (\hat{i} - 2 \hat{j} + \hat{k}) + λ (2 \hat{i} + 3 \hat{j} - 5 \hat{k}) .$

Open in App

Solution

The given line is parallel to the vector $2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ and the required line is parallel to the given line.
So, the required line is parallel to the vector $2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ .

Hence, the equation of the required line passing through the point (2, $-$ 1, 3) and parallel to the vector $2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ is $\vec{r} = (2 \hat{i} - \hat{j} + 3 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} - 5 \hat{k})$ .

Suggest Corrections

Similar questions

(2, - 1, 3)

r = i + j - k + λ (2 i - 2 j + k)

r = 2 i - j - 3 k + μ (i + 2 j + 2 k)

\vec{r} = (- 2 \hat{i} + 3 \hat{j}) + λ (2 \hat{i} - 3 \hat{j} + 6 \hat{k}) .

(3, - 1, 2)

$¯ ¯ ¯ r = ¯ i + ¯ j - ¯ ¯ ¯ k + λ (2 ¯ i - 2 ¯ j + 2 ¯ ¯ ¯ k)$ and $¯ ¯ ¯ r = 2 ¯ i + ¯ j - 3 ¯ ¯ ¯ k + μ (¯ i - 2 ¯ j + 2 ¯ ¯ ¯ k)$

\vec{r} = \hat{i} + 2 \hat{j} - 4 \hat{k} + λ (2 \hat{i} + 3 \hat{j} + 6 \hat{k}) and, \vec{r} = 3 \hat{i} + 3 \hat{j} - 5 \hat{k} + μ (2 \hat{i} + 3 \hat{j} + 6 \hat{k})

r = (i + j - k) + λ (2 i - 2 j + k)

r = (2 i - j - 3 k) + μ (i + 2 j + 2 k)

Join BYJU'S Learning Program