The vector equation of the symmetrical form of equation of straight line x - 5 3 = y + 4 7 = z - 6 2 is:

Question

The vector equation of the symmetrical form of equation of straight line $\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{z - 6}{2}$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $\vec{r} = (5 \hat{i} - 4 \hat{j} + 6 \hat{k}) + μ (3 \hat{i} + 7 \hat{j} + 2 \hat{k})$

Explanation:

$\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$ have vector form

$\vec{r} = (x_{1} \hat{i} + y_{1} \hat{j} + z_{1} \hat{k}) + λ (a \hat{i} + b \hat{j} + c \hat{k})$

Required equation in vector form is

$\vec{r} = (5 \hat{i} - 4 \hat{j} + 6 \hat{k}) + μ (3 \hat{i} + 7 \hat{j} + 2 \hat{k})$

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