Question

Find the angle between two vectors Ā= 2i + j -k and B = i - K.

Step by step explanation, surely marked as brainliest. ​

Answer 1

Answer:

$\theta$ = 30°

Step-by-step explanation:

The angle between two vectors can be found with the following formula:-

cos $\theta$ = $\frac{\vec{A}.\vec{B}}{\vec{|A|} \vec{|B|}}}$

Here,

$\vec{A}.\vec{B}$ is the Dot Product of the two vectors

$\vec{|A|} \vec{|B|}$ is the product of the magnitude of the two vectors.

Magnitude of $\vec{A}$ :-

=$\sqrt{2^2+1^2+(-1)^2}$

=$\sqrt{4+1+1}$

=$\sqrt{6}$

Magnitude of $\vec{B}$ :-

=$\sqrt{1^2+0^2+(-1)^2}$

=$\sqrt{1+1}$

=$\sqrt{2}$

Dot Product of two vectors:-

= $\vec{A}.\vec{B}$

= $(2 \hat{ \imath } + \hat{ \jmath } - \hat{ k })(1 \hat{ \imath } + 0 \hat{ \jmath } - \hat{ k })$

= 2 + 1

= 3

Substitute the values:-

cos $\theta$ = $\frac{3}{\sqrt{6} \times \sqrt{2}}$

cos $\theta$ = $\frac{3}{\sqrt{12}}$

cos $\theta$ = $\frac{3}{2\sqrt{3}}$

cos $\theta$ = $\frac{\sqrt{3} \times \sqrt{3}}{2\sqrt{3}}$

cos $\theta$ = $\frac{\sqrt{3}}{2}$

$\theta$ = 30°

So, the angle between the two vectors is 30°

$\large\boxed{\large\boxed{\large\boxed{Solved !}}}}$