Question

If a vector = 2i cap - 2j cap - k cap and b vector = i cap + j cap then find angle between a vector nd b vector

Answer 1

Answer:

The angle between $\vec{a}\:and\:\vec{b}$ is $\frac{\pi}{2}$

Step-by-step explanation:

Formula used:

The angle between $\vec{a}\:and\:\vec{b}$ is

$cos\theta=\frac{\vec{a}.\vec{b}}{|\vec{a}|\:|\vec{b}|}$

Given:

$\vec{a}=2\vec{i}-2\vec{j}-\vec{k}$

$\vec{b}=\vec{i}+\vec{j}+0\vec{k}$

$\vec{a}.\vec{b}=(2)(1)+(-2)(1)+(-1)(0)$

$\vec{a}.\vec{b}=2-2+0=0$

Now,

$cos\theta=\frac{\vec{a}.\vec{b}}{|\vec{a}|\:|\vec{b}|}$

$\implies\:cos\theta=\frac{0}{|\vec{a}|\:|\vec{b}|}$

$\implies\:cos\theta=0$

$\implies\:\theta=\frac{\pi}{2}$