Posted by **manpreet** on Friday, November 23, 2012 at 4:32pm.

If a and b are two unit vectors and θ is the angle between them, then a+b is a unit vector if θ is

- dps -
**Steve**, Friday, November 23, 2012 at 6:35pm
without loss of generality, we can let

a = <1,0>

b = <cosθ,sinθ>

a+b = <(1+cosθ),sinθ>

|a+b|^2 = (1+cosθ)^2 + sin^2 θ

if a+b is a unit vector,

|a+b|^2 = 1

1+2cosθ+cos^2θ + sin^2θ = 1

1+2cosθ = 0

cosθ = -1/2

θ = 2pi/3

## Answer This Question

## Related Questions

- Precalc - Suppose vector a is 3 units long, the magnitude of vector b is 1 units...
- Math (Geometry-Vectors) - Let θ be the angle between two vectors v and u . ...
- precalculus - the following is a point not on a unit circle. θ → (-5,...
- Physics - Consider three force vectors ~ F1, ~ F2, and ~ F3. The vector ~ F1 has...
- PHYSICS - A placekicker is about to kick a field goal. The ball is 20.1 m from ...
- Prabhat academy - If vector a & vector b are unit vectors ,then what is the ...
- Complex angles - There are four complex fourth roots to the number 4−43&#...
- trig - Question #1 Suppose that θ is an angle in standard position whose ...
- Math - Calculus - The identity below is significant because it relates 3 ...
- science - The most convenient way to express vectors in the two dimensional ...

More Related Questions