we are given with
v=<-7,8> and w=<5,3>
1) Using the formula [tex] \\
\
v_1*v_2=|v_1||v_2|cos\theta\\
\\
\
\Rightarrow cos \theta=\frac{v_1*v_2}{|v_1||v_2|}\\ [/tex]
[tex] \\
\
v_1*v_2=|v_1||v_2|cos\theta\\
\\
\
\Rightarrow cos \theta=\frac{<-7,8>*<5,3>}{|\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}\\ [/tex]
Answer:[tex]\theta =100.22^{\circ}[/tex]
Step-by-step explanation:
vector v is -7i+8j
vector w is 5i+3j
Angle between vectors is given by
[tex]a\cdot b=|a||b|cos\theta [/tex]
therefore applying above formula
[tex]v\cdot w=|v||w|cos\theta [/tex]
-35+24=[tex]\sqrt{7^2+8^2}\sqrt{5^2+3^2}cos\theta [/tex]
[tex]\frac{-11}{61.983}=cos\theta [/tex]
[tex]cos\theta =-0.1774[/tex]
[tex]\theta =100.22^{\circ}[/tex]
