Question

if teeta is the angle between the vectors ICAP + 3 J cap + 7 k cap and ICAP - 3 J cap + K cap then cos theta is equal to

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Vectors are}$

$\mathsf{\hat{i}+3\hat{j}+7\hat{k}\;\;\&\;\;\hat{i}-3\hat{j}+\hat{k}}$

$\underline{\textsf{To find:}}$

$\textsf{The angle between the given two vectors}$

$\underline{\textsf{Solution:}}$

$\textsf{Let}$

$\mathsf{\vec{a}=\hat{i}+3\hat{j}+7\hat{k}}$

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

$\mathsf{\vec{a}.\vec{b}=1(1)+3(-3)+7(1)}$

$\mathsf{\vec{a}.\vec{b}=8-9=-1}$

$\mathsf{|\vec{a}|=\sqrt{1^2+3^2+7^2}=\sqrt{1+9+49}=\sqrt{59}}$

$\mathsf{|\vec{b}|=\sqrt{1^2+(-3)^2+1^2}=\sqrt{1+9+1}=\sqrt{11}}$

$\textsf{Since}\;\mathsf{\theta}\;\textsf{is the angle between the given vectors, we have}$

$\mathsf{cos\theta=\dfrac{\vec{a}.\vec{b}}{|\vec{a}|\;|\vec{b}|}}$

$\mathsf{cos\theta=\dfrac{-1}{\sqrt{59}\,\sqrt{11}}}$

$\mathsf{\theta=cos^{-1}(\dfrac{-1}{\sqrt{59}\,\sqrt{11}})}$

$\textsf{which is the angle between given vectors}$

Find more:

If vector A=2i+2j+3k and vector B=3i-2j-4k, find cross product and angle b/w A and B?​

https://brainly.in/question/22534241