Question

The vector equation of the line ${\displaystyle \frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}}$ is ${\displaystyle \overrightarrow{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda (3\hat{\text{i}}+7\hat{\text{j}}+2\hat{\text{k}})}$.

पर्याय

• True

• False

Answer 1

This statement is True.

Explanation:

The Cartesian form of the equation is ${\displaystyle \frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}=\lambda }$

∴ Here x₁ = 5

y₁ = – 4

z₁ = 6,

a = 3

b = 7

c = 2

So, the vector equation is ${\displaystyle \overrightarrow{\text{r}}=(5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}})+\lambda (3\hat{\text{i}}+7\hat{\text{j}}+2\hat{\text{k}})}$