Question

rotate the vector $\langle 3,-2\
angle$ $90^{\circ}$ degrees counterclockwise about the origin. $\langle$, $\
angle$

Explanation:

Step1: Recall the rotation formula

For a vector \(\langle x,y
angle\) rotated \(90^{\circ}\) counter - clockwise about the origin, the new vector is \(\langle -y,x
angle\).

Step2: Apply the formula

Given \(x = 3\) and \(y=-2\). Substitute \(y\) and \(x\) into the formula. The new \(x\) - coordinate is \(-y=-(-2) = 2\), and the new \(y\) - coordinate is \(x = 3\).

Answer:

\(\langle 2,3
angle\)