Given that p = (-5, 11) and q = (-6, 4), find the component form and magnitude of vector qp. < -11, 7> , square root of 38 < -1, -7> , square root of 50 < 1, 7> , 50 < 1, 7> , square root of 50

We'll use the Pythagorean Theorem (otherwise known as the Distance Formula):

Going from Q to P, x increases by 1 and y increases by 7. Thus, the component form of QP is <1,7>, and the magnitude of this vector is √(1^2+7^2) = 5√2.

Note: this is equivalent to <1, 7>, square root of 50.

a negative exponent is translated as follows:

so, we have