What Is the Angle Between Two Vectors with Equal Magnitudes?

[moonworn]

Homework Statement

Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A + B to be 100 times larger than the magnitude of A - B, what must be the angle between them?

Homework Equations

The Attempt at a Solution

I am completely lost. Vectors are a completely new subject to me. I am not familiar with vector algebra notation yet as we haven't yet covered it, but I assume we are to solve this visually/conceptually given what we do know. Any help where to start?

 

[dextercioby]

HINT: The scalar product between A+B and A-B is 0, since the 2 vectors are perpendicular.

Daniel.

 

[moonworn]

Hrm maybe if I had a step by step explanation I would understand what was going on. I didn't even know what "vector" was yesterday. I appreciate the hint daniel, but I still have no idea.

 

[chanvincent]

HINT: The scalar product between A+B and A-B is 0, since the 2 vectors are perpendicular.

Sorry... A and B are not perpendicular

EDIT:

Hints: |A+B| = 100 |A-B|

notice |A+B|^2 = (A+B) dot (A+B) and
A dot B = |A| |B| cos \theta

 

[AlephZero]

HINT: The scalar product between A+B and A-B is 0, since the 2 vectors are perpendicular.

This seems backwards: actually A+B and A-B are perpendicular (i.e. they have scalar product zero) because A and B are equal magnitude.

Moonworm, if you are just starting vectors, draw a diagram with two vectors from a point, with equal magnitude, and an angle theta between them. Then draw the vectors a+b (using the parallelogram rule) and a-b.

You can find the lengths of a+b and a-b using geometry and trig.