February 20, 2017

Homework Help: Math please help

Posted by Anonymous on Sunday, March 30, 2008 at 9:27am.

For the first question I really need all help I can get. Thanks!

1. Given a and b are unit vectors,

a) if the angle between them is 60 degrees, calculate (6a+b) . (a-2b)

b) if |a+b| = sqrt3, determine (2a-5b) . (b+3a)

2. The vectors a = 3i - 4j - k and b = 2i + 3j - 6k are the diagonals of a parallelogram. Show that this parallelogram is a rhombus, and determine the lengths of the sides and angles between the sides.

3. If a and b are perpendicular, show that |a|^2 + |b|^2 = |a + b|^2. What is the usual name of this result.

b) If a and b are not perpendicular, and a-b = c, express |c|^2 in terms of a and b. What is the usual name of this result?

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