Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

If $\vec a$ is a non-zero vector, then always

Options:

$\vec a.\vec a=0$

$\vec a.\vec a>0$

$\vec a.\vec a<0$

$\vec a.\vec a=1$

Correct Answer:

$\vec a.\vec a>0$

Explanation:

The correct answer is Option (2) → $\vec a.\vec a>0$

Given: $\vec{a}$ is a non-zero vector.

Then, $\vec{a} \cdot \vec{a} = |\vec{a}|^2$

Since $\vec{a} \ne \vec{0} \Rightarrow |\vec{a}| > 0 \Rightarrow |\vec{a}|^2 > 0$

∴ $\vec{a} \cdot \vec{a} > 0$