Question

Find a unit vector perpendicular to each of the vectors( a+b)( a-b) where a=3i^+2j^+2k^ and b=i^+2j^-2k^

Answer 1

$\bigstar$ EXPLAINATION $\star$

• Given

$\vec{a}$ = $3 \hat{\imath}$ + $2 \hat{\jmath}$ + $2 \hat{k}$

$\vec{b}$ = $1 \hat{\imath}$ + $2 \hat{\jmath}$ + $-2 \hat{k}$

• To find

Unit vector perpendicular to $\vec{a + b}$ as well as $\vec{a - b}$

• How to find

As we know that $\vec{a + b}$ and $\vec{a - b}$ lie on the same plane as $\vec{a}$ and $\vec{b}$

So in the question they are asking the unit vector perpendicular to the plane where $\vec{a}$ and $\vec{b}$ lies

So we have to cross product of $\vec{a}$ and $\vec{b}$

Then we have of find unit vector in the direction of cross product of $\vec{a}$ and $\vec{b}$

• Procedure

$\vec{a}$ $\times$ $\vec{b}$ = ($3 \hat{\imath}$ + $2 \hat{\jmath}$ + $2 \hat{k}$) $\times$ ($1 \hat{\imath}$ + $2 \hat{\jmath}$ + $-2 \hat{k}$)

[tex] \begin{array}{ c c c } i & j & k \\ 3 & 2 & 2 \\ 1 & 2 & -2 [\tex]