SOLUTION: [p] = 3 [q] = 4 p . q = 10 Find the value of q.(p + q) I am unsure of the square bracket around the letters p and q. Multiplied out:- q.p + q^2 4 x 3 + 4^2 = 28 but a

Question 1207272: [p] = 3 [q] = 4
p . q = 10
Find the value of
q.(p + q)
I am unsure of the square bracket around the letters p and q.
Multiplied out:-
q.p + q^2
4 x 3 + 4^2
= 28
but answer is 26!
Can you help me please?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

q . (p + q)
= q . p + q . q
= q . p + |q|^2
= 10 + 4^2
= 26

The square brackets appear to refer to the magnitude or length of the vector. Instead of [q] I used the notation |q|
When you dot product a vector with itself, the result is the square of the magnitude of that vector.
In this case we have: q.q = |q|^2
A short proof can be done through use of the Pythagorean Theorem.

Keep in mind that p . q = 10 is given and it is the same as q . p = 10 since we can dot product any two vectors in either order.
q.p is not the same as |q| times |p|

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