Question

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

1) Use the formula v1*v2=|v1||v2|cos(theta) to find the cosine of the angle between these vectors.
2)Use the cosine of the angle to find the actual angle between the two vectors.

Answer 1

we are given with

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

1) Using the formula
`image`

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Answer 2

Answer:
`\theta =100.22^(\circ)`

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=
`√(7^2+8^2)√(5^2+3^2)cos\theta`

`(-11)/(61.983)=cos\theta`

`cos\theta =-0.1774`

`\theta =100.22^(\circ)`