(\(\vec{a}\) - \(\vec{b}\)) ×

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

(\(\vec{a}\) - \(\vec{b}\)) ×(\(\vec{a}\)+\(\vec{b}\)) is equal to-

Options:

(\(\vec{a}\) × \(\vec{b}\))

- (\(\vec{a}\) × \(\vec{b}\))

-2 (\(\vec{a}\) × \(\vec{b}\))

2 (\(\vec{a}\) × \(\vec{b}\))

Correct Answer:

2 (\(\vec{a}\) × \(\vec{b}\))

Explanation:

(\(\vec{a}\) - \(\vec{b}\)) × (\(\vec{a}\) + \(\vec{b}\)) = (\(\vec{a}\) - \(\vec{b}\)) × \(\vec{a}\) + (\(\vec{a}\) - \(\vec{b}\)) × \(\vec{b}\)

= (\(\vec{a}\) × \(\vec{a}\)) -(\(\vec{b}\) × \(\vec{a}\)) + (\(\vec{a}\)×\(\vec{b}\))- (\(\vec{b}\) × \(\vec{b}\) )

= \(\vec{0}\)+ (\(\vec{a}\)× \(\vec{b}\)) + (\(\vec{a}\) ×\(\vec{b}\) )- \(\vec{0}\)

= 2 (\(\vec{a}\)× \(\vec{b}\))