If $|\vec{a}|=5, |\vec{b}|=2$ and $|\vec

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

If $|\vec{a}|=5, |\vec{b}|=2$ and $|\vec{a}.\vec{b}|=8$ then the value of $|\vec{a}×\vec{b}|$ is :

Options:

±6

Correct Answer:

Explanation:

The correct answer is Option (2) → 6

$|\vec{a}.\vec{b}|=8$

$=|\vec{a}||\vec{b}|\cos θ=8$

$\cos θ=\frac{4}{5}$

$⇒\sin θ=\frac{3}{5}$

so $|\vec{a}×\vec{b}|=|\vec{a}||\vec{b}|\sin θ=5×2×\frac{3}{5}=6$