Question

What is the angle between v=(-7,8) and w=(5,3)

Answer 1

we are given with

v=<-7,8> and w=<5,3>

1) Using the formula $\\ \ v_1*v_2=|v_1||v_2|cos\theta\\ \\ \ \Rightarrow cos \theta=\frac{v_1*v_2}{|v_1||v_2|}$

$\\ \ v_1*v_2=|v_1||v_2|cos\theta\\ \\ \ \Rightarrow cos \theta=\frac{*}{|\sqrt{49+64}||\sqrt{25+9}|}\\ \\ \Rightarrow cos \theta=\frac{-35+24}{|\sqrt{49+64}||\sqrt{25+9}|}=\frac{-11}{|\sqrt{113}||\sqrt{34}|}\\ \\ \ \Rightarrow cos \theta=-0.1774\\ \\ \ 2.\\ \\ \ cos \theta=-0.1774\\\\\\ \ \Rightarrow \theta=cos^{-1}(-0.1774)\\ \\ \ \Rightarrow \theta=100.21^{\circ}$

Answer 2

Answer:$\theta =100.22^{\circ}$

Step-by-step explanation:

vector v is -7i+8j

vector w is 5i+3j

Angle between vectors is given by

$a\cdot b=|a||b|cos\theta$

therefore applying above formula

$v\cdot w=|v||w|cos\theta$

-35+24=$\sqrt{7^2+8^2}\sqrt{5^2+3^2}cos\theta$

$\frac{-11}{61.983}=cos\theta$

$cos\theta =-0.1774$

$\theta =100.22^{\circ}$