Answer and Step-by-step explanation:
We see that the vector is written a QP.
Usually, when finding the vector in component form, it is in this form.
PQ = < q1 - p1,q2 - p2> = <v1,v2> = v
In this situation, Q and P are switched.
QP = < p1 - q1, p2 - q2> = <v1,v2> = v
Now, we plug in our values.
QP = < -5 - -6, 11 - 4 > = < 1 , 7 >
The component form of our vector is <1, 7>
To find the magnitude, we do this:
\(||v|| = \sqrt{(p1 - q1)^2 + ( p2 - q2)^2} = \sqrt{(v1)^2+ (v2)^2}\)
We already got the first part of this formula, so we plug in our vector into the second portion of the formula.
\(||v|| = \sqrt{(1)^2 + (7)^2} \\\\\\||v|| = \sqrt{1 + 49} \\\\\\||v|| = \sqrt{50} \\\\\\\)
This simplifies down to \(2\sqrt{5}\), but the answer choice we are given shows \(\sqrt{50}\)
The magnitude of vector QP is \(\sqrt{50}\).
#teamtrees #PAW (Plant And Water)
