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

Answer:

148.67

Step-by-step explanation:

Angle between two vectors is equal to

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

$x = \cos {}^{ - 1} ( \frac{v \times v_{2} }{ |v| |v _{2} | } )$

Let first, find the dot product

$< - 2,5 > \times < 4, - 3 > = - 8 - 15 = - 23$

Next we find magnitudes

$- 2 {}^{2} + {5}^{2} = x {}^{2}$

$29 = {x}^{2}$

$x = \sqrt{29}$

${4}^{2} + {3}^{2} = {x}^{2}$

$25 = {x}^{2}$

$x = 5$

So the we are now,

$\cos {}^{ - 1} ( \frac{ - 23}{ 5\sqrt{29}} )$

We then get

$148.67$