Question

If vectors $\overrightarrow{ a }_{1}= x \hat{ i }-\hat{ j }+\hat{ k }$ and $\overrightarrow{ a }_{2}=\hat{ i }+\hat{ y } \hat{ j }+ z \hat{ k }$ are collinear, then a possible unit vector parallel to the vector $\hat{\hat{i}}+\hat{ y }+ z \hat{ k }$ is

• A. $\frac{1}{\sqrt{2}}(-\hat{ j }+\hat{ k })$
• B. $\frac{1}{\sqrt{2}}(\hat{ i }-\hat{ j })$
• C. $\frac{1}{\sqrt{3}}(\hat{ i }+\hat{ j }-\hat{ k })$
• D. $\frac{1}{\sqrt{3}}(\hat{ i }-\hat{ j }+\hat{ k })$

Answer 1

Answer: (D)

$\vec{ a }_{1}$ and $\vec{ a }_{2}$ are collinear
so $\frac{x}{1}=\frac{-1}{y}=\frac{1}{z}$
unit vector in direction of
$x \hat{i}+y \hat{j}+z \hat{k}=\pm \frac{1}{\sqrt{3}}(\hat{i}-\hat{j}+\hat{k})$