Question

Question 4 of 13

if v = (-2,5) and V2 = (4,-3), then the angle between the two vectors is
Round your answer to two decimal places.


please i need help asap

Answer 1

148.67

Explanation:

Angle between two vectors is equal to

Inverse cosine of their vectors dot product/ their magnitudes multiplied.

`x = \cos {}^( - 1) ( (v * v_(2) )/( |v| |v _(2) | ) )`

Let first, find the dot product

`< - 2,5 > * < 4, - 3 > = - 8 - 15 = - 23`

Next we find magnitudes

`- 2 {}^(2) + {5}^(2) = x {}^(2)`

`29 = {x}^(2)`

`x = √(29)`

`{4}^(2) + {3}^(2) = {x}^(2)`

`25 = {x}^(2)`

`x = 5`

So the we are now,

`\cos {}^( - 1) ( ( - 23)/( 5√(29)) )`

We then get

`148.67`