Question

show the vector a vector is equal to two ICAP + 3 J cap + 6 k cap, b vector is equal to 3 ICAP - 6 J cap + 2 k cap and C vector is equal to 6 ICAP + 2 J cap - 3 k cap and mutually perpendicular ​

Answer 1

Answer with Explanation:

We are given that

$\vec{a}=2\hat{i}+3\hat{j}+6\hat{k}$

$\vec{b}=3\hat{i}-6\hat{j}+2\hat{k}$

$\vec{c}=6\hat{i}+2\hat{j}-3\hat{k}$

We have to prove that given vectors are mutually perpendicular.

$\vec{a}\cdot\vec{b}=(2i+3j+6k)\cdot(3i-6j+2k)=6-18+12=0$

$\vec{b}\cdot \vec{c}=(3i-6j+2k)\cdot(6i+2j-3k)=18-12-6=0$

$\vec{a}\cdot\vec{c}=(2i+3j+6k)\cdot(6i+2j-3k)=12+6-18=0$

Hence, vector a , b and c are mutually perpendicular.