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

Moderate

A

$\bar{r} = (5 \bar{i} + 4 \bar{j} + 6 \bar{k}) + λ (3 \bar{i} + 2 \bar{j} + 2 \bar{k})$
B

$\bar{r} = (5 \bar{i} - 4 \bar{j} + 6 \bar{k}) + λ (3 \bar{i} + 7 \bar{j} + 2 \bar{k})$
C

$\bar{r} = (5 \bar{i} + 4 \bar{j} + 6 \bar{k}) + λ (3 \bar{i} + 7 \bar{j} + 2 \bar{k})$
D

$\bar{r} = (- 5 \bar{i} + 4 \bar{j} + 6 \bar{k}) + λ (3 \bar{i} + 7 \bar{j} + 2 \bar{k})$

Solution

$\frac{x - 5}{3} - \frac{y + 4}{7} = \frac{z - 6}{2} = λ x = 5 + 3 λ, y = - 4 + 7 λ, z = 6 + 2 λ \overset{\leftrightarrow}{r} = x \overset{⇀}{i} + y \overset{⇀}{j} + z \vec{k s u b t u t e}$

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