# Maths

posted by .

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 -

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)

## Similar Questions

1. ### Physics (vectors)

Given vectors A= (Axi + Ayj), B= (Byj+Bzk) and C= (Cyj + Czk). a) find the triple product of these vectors defined by A dot (BxC) in terms of the vector components. I get 0 as the answer. b) is the result found in a) a scalar of a …
2. ### Math: Vectors

I forgot how to do the following, so I'm not sure if they're correct or not: Find the work done by a force "F" that causes a displacement "d". i and j = unit vectors a) F = 4i + j d = 3i + 10j W = (4i + j)(3i + 10j) W = 12|i|^2 + 40ij …
3. ### Physics

Using the definition of the scalar product, find the angles between the following pairs of vectors. A = - 4 i + 2 j + 2 k and B = - 3 j - 3 k I understand to do [(A).(B)]/|A|*|B| = cos theta; but I'm getting 0 for |A| and don't know …
4. ### AP Physics

Find the scalar product of the vectors in Figure P7.8, where è = 117° and F = 31.0 N. y | | ___| Unk Angle----> / | -------\--------------x starts@O-----> / /| / / /_|/<-----117 degrees / / | / / <-----31.0N
5. ### physics

The magnitude of the scalar product of vectors A and B is three times as large as the magnitude of the vector product of the same two vectors. If they were placed tail-to-tail in space, A and B would form an angle of approximately …
6. ### UNIVERSITY PHYSICS 1

Find the magnitude of vectors A=?+4j+4k B=?
7. ### UNIVERSITY PHYSICS 1

find the magnitude of vectors A=?+4j+4k B=?
8. ### university physics

find the magnitude of vectors A=?+4j+4k B=?
9. ### Physics

Find the scalar product of the vectors ai+bj and bi-aj . Where a and b are arbitrary constants. What's the angle between the two vectors?
10. ### Math - vectors

For what value of t are these two vectors parallel?

More Similar Questions