Question

What is the magnitude of w?
(-8, 3) W
|W| = [?]
Round to the nearest hundredth.

Answer 1

The magnitude of W is 8.54

Explanation:

The magnitude of a vector is the length of the line segment that represents the vector. To calculate the magnitude of a vector in two dimensions, we can use the following formula:

|W| = sqrt(W_x^2 + W_y^2)

where W_x and W_y are the components of the vector W in the x- and y-directions, respectively.

For the vector W = (-8, 3), the magnitude is:

|W| = sqrt((-8)^2 + 3^2) = sqrt(73) = 8.54 (rounded to the nearest hundredth)

Therefore, the magnitude of W is 8.54.

Answer 2

`w = < \stackrel{ x }{-8}~~,~~\stackrel{ y }{3} > \hspace{5em}||w||=√(x^2 + y^2) \\\\\\ ||w||=√((-8)^2 + 3^2)\implies ||w||=√(64+9)\implies ||w||=√(73)\implies ||w||\approx 8.54`