Posted by **Anique** on Monday, March 14, 2011 at 11:05am.

There are 3 vectors:

p= 7i + 10j

q= 3i + 12j

r= -i +4j

Could you show me how to find the angle PQR. using the scalar product.

- Maths -
**Reiny**, Monday, March 14, 2011 at 1:58pm
I will associate your vectors to have endpoints

P(7,10), Q(3,12) and R(-1,4)

then vector(PQ) = (-4,2)

vector(QR) = (-4,-8)

then PQ.QR = |PQ||QR|cos(theta), where theta is the angle between them

16-16 = |PQ||QR|cos(theta)

cos(theta) = 0

theta = 90 degrees

(notice the slope of lines PQ and QR are negative reciprocals of each other, so PQ and QR are perpendicular)

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