Sunday

December 21, 2014

December 21, 2014

Posted by **Anonymous** on Monday, March 3, 2008 at 3:17pm.

| a × b |² + (a • b)² = |a|²|b|²

My work, LSH:

= | a × b |² + (a • b)²

= (|a||b|sinθ)(|a||b|sinθ) + (|a||b|cosθ)(|a||b|cosθ)

= (|a|²)(|a||b|)(|a|sinθ)(|a||b|)(|b|²)(|b|sinθ)(|a| sinθ)(|b|sinθ)(sin²θ) + (|a|²)(|a||b|)(|a|cosθ)(|a||b|)(|b|²)(|b|cosθ)(|a| cosθ)(|b|cosθ)(cos²θ)

= (|a|²)(|a||b|)²(|a|sinθ)²(|b|²)(|b|sinθ)²(sin²θ) + (|a|²)(|a||b|)²(|a|cosθ)²(|b|²)(|b|cosθ)²(cos²θ)

= (|a|²|b|²(|a||b|)²) [(|a|sinθ)²(|b|sinθ)²(sin²θ) + (|a|cosθ)²(|b|²)(|b|cosθ)²(cos²θ)]

= (|a|²|b|²(|a||b|)²) [(|a|²)(sin²θ)(|b|²)(sin²θ)(sin²θ) + (|a|²)(cos²θ)(|b|²)(|b|²)(cos²θ)(cos²θ)]

= (|a|²|b|²(|a||b|)²) [(sin²θ)(sin²θ)(sin²θ) + (cos²θ)(cos²θ)(cos²θ)]

And now I don't know what else to do! Please help. Did I mess up somewhere in my steps? Or is it possible to common factor still?

- Math - Calculus -
**Count Iblis**, Monday, March 3, 2008 at 5:07pmMy work, LSH:

= | a × b |² + (a • b)²

= (|a||b|sinθ)(|a||b|sinθ) + (|a||b|cosθ)(|a||b|cosθ)

You can write this as:

|a|^2|b|^2[sin^2(theta) + cos^2(theta)]

The result follows from the fact that

sin^2(theta) + cos^2(theta) = 1

**Answer this Question**

**Related Questions**

calculus - Find two unit vectors that make an angle of 60° with v = ‹3, 4›. Give...

Physics - 2. We have two vectors that line in the x-y plane. If we take the ...

Math - Product Dot Vectors - How would you expand and simplify the following ...

12th grade - prove that normal to plane containing 3 points whose position ...

PHYSICS VECTORS - 1. The problem statement, all variables and given/known data ...

Calculus - Two force vectors act on an object and the dot product of the two ...

Vectors - When do you use the dot product and the cross product?

Mamthematics - Vectors - a) If vector u and vector v are non-collinear vectors ...

Physics - 1. Consider the two vectors P and Q. The definition of P is P = &#...

Calculus - I am asked this: How can you do the cross product of two-dimensional ...