# Physics: Vectors & their scalar product

1. May 19, 2013

### sakau2007

1. The problem statement, all variables and given/known data
Given the vectors:
P = 8i +5j-Pzk m
and
Q = 3i -4j-2k m
Determine the value of Pz so that the scalar product of the two vectors will be 60m2

2. Relevant equations
Sure seems like we will need to use the following equation:
P * Q = |P| * |Q| * cos ∅

But I don't recall being able to be taught the angle between two vectors so cos would still be unknown?

3. The attempt at a solution

Also, I assume the scalar product being 60 means that PQ = 60, or that:
Q = √32+-42+22 = √29
So, P would be 60/√29

Then this equation should be solved such as
60/√29 = √82+52+(-Pz)2

11.14172029 = √82+52+(-Pz)2

124.13793 = 89 + (-Pz)2

35.13793 = (-Pz)2

This would give an answer of about +/- 5.92, but in my solution manual I see that the solution is -28. Where have I gone wrong?

2. May 19, 2013

### consciousness

Your job would be simplified by the "Distributive property of dot product".

3. May 19, 2013

### Staff: Mentor

Here's a hint:

The scalar product of i with i is equal to ??

The scalar product of i with j is equal to ??

The scalar product of i with k is equal to ??

4. May 19, 2013

### sakau2007

It was me not understanding what scalar product was in solving this.

When the scalar product of PQ is said to be 60, that means that:
(8*3) + (5*-4)+(2*-Pz) = 60
Solving that simple equation yields the correct answer of -28.