- #1
DespicableMe
- 41
- 0
Homework Statement
a) Write the cosine law using a vector operation.
b) If |vector a - vector b| = |vector a + vector b|, prove that a is perpendicular to b using the formula you found in a).
The Attempt at a Solution
The red period represents the dot product
a) magnitude c = SQUAREROOT (a.a + b.b - 2(a.b) )
b) magnitude c = SQUAREROOT (a.a + b.b - 2(a.b) )
= SQUAREROOT ( a2 + b2 - 2( |a||b|cos 90 )
= SQUAREROOT ( a2 + b2 )
And this is the Pythagorean theorem, which only applies for right angle triangles, so if mag. C is SQUARERT (a2+b2), then a and b are perpendicular.
DId I do this correctly?
I didn't know how to include |vector a - vector b| = |vector a + vector b| into the equation and it only asked to prove it using the formula that I found...