Question

the position vectors of points P and Q are given by r1= 2i + 3j - k and r2= 4i - 3j + 2k. Determive PQ in terms of i,j,k and find its magnitude.

Answer 1

P= <2i , 3j , -k>
Q= <4i , -3j , 2k>
P*Q in terms of i, j, k is pretty simple. Just multiply the two i terms to get a new i term, multiply the j terms to get a new one, multiply the k terms to get a new k, then put them in order:
New Vector
=
<(2i)(4i) , (3j)(-3j) , (-k)(2k)>
=
<8i , -6j , -2k>

In order to get the MAGNITUDE of P*Q, what you do is multiply like terms and add them together:
(2i)(4i) + (3j)(-3j) + (-k)(2k)
=
(8) + (-6) + (-2)
=
8-6-2
=
0

I think that should be right.

Answer 2

3(-3) is not equal to 6

Answer 3

You're right. It's equal to (-6), like I said.

Answer 4

If you are adding a negative number, it's the same as subtracting the positive number.