Question

Х If ő is unit vector then (a.b)6 + 5 x (ä x b) is equal to a) à 2.5 b) (a.ba c) d) None of these​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\mapsto\,\,\vec{b}\,\,\rm{is\,\,a\,\,unit\,\,vector}$

Now,

$\left(\vec{a}\,\cdot\,\vec{b}\right)\vec{b}+\vec{b}\times\left(\vec{a}\,\times\,\vec{b}\right)$

Using vector tripple product, we have,

$=\left(\vec{a}\,\cdot\,\vec{b}\right)\vec{b}+\left(\vec{b}\,\cdot\,\vec{b}\right)\vec{a}-\left(\vec{b}\,\cdot\,\vec{a}\right)\vec{b}$

We know, dot product is commutative, so,

$=\left(\vec{a}\,\cdot\,\vec{b}\right)\vec{b}+\left(\vec{b}\,\cdot\,\vec{b}\right)\vec{a}-\left(\vec{a}\,\cdot\,\vec{b}\right)\vec{b}$

$=\left(\vec{b}\,\cdot\,\vec{b}\right)\vec{a}$

$=\left|\vec{b}\right|^{2}\cdot\vec{a}$

$=1\cdot\vec{a}$

$=\vec{a}$