Question

Given v=3i-j and w=9i 2j finde the angle between v and w.

Answer 1

The angle between vectors
`v=3i-j and w=9i+2j` is found using the dot product and the magnitude of each vector, then taking the inverse cosine of their ratio to obtain the angle.

Step-by-step explanation:

To find the angle between the two vectors
`v=3i-j and w=9i+2j`, we can use the dot product formula which relates the dot product of two vectors to the cosine of the
`angle (θ)` between them:

`v · w = |v| |w| cos(θ)`

First, calculate the dot product of v and w:

`v · w = (3i - j) · (9i + 2j) = 3*9 + (-1)*2 = 27 - 2 = 25`

Next, find the magnitude of each vector:

`|v| = √(3² + (-1)²) = √(9 + 1) = √10|w| = √(9² + 2²) = √(81 + 4) = √85`

Now, calculate the cosine of the angle:

`cos(θ) = (v · w) / (|v| |w|) = 25 / (√10 * √85)`

Finally, to find the angle θ, we take the inverse cosine:

`θ = cos⁻¹(25 / (√10 * √85))`

Calculate the value of
`θ` using a calculator to get the final answer in degrees.