Maths. Section B1Vectors

( a - b ) ×( a + b ) is equal to-

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

Answer & explanation

Correct answer: option 4

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

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

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

= 2 (\(\vec{a}\)× \(\vec{b}\))