Thursday

December 18, 2014

December 18, 2014

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

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?

- Math please help -
**Reiny**, Sunday, March 30, 2008 at 11:17amYou seem to post quite a few vector questions under the name of anonymous.

Are you the same person?

Please use a first name or some other nick to identify yourself.

Your first question uses the basic laws of vectors.

(2a-5b)∙(b+3a) = 2a∙b + 6│a│^2 - 5│b│^2 - 15a∙b

= 6│a│^2 - 5│b│^2 - 13a∙b

we know │a│ and │b│ are 1 each and

a∙b = │a││b│cos60º

a∙b = 1*1*1/2

so 6│a│^2 - 5│b│^2 - 13a∙b

= 6*1 - 5*1 - 13*1/2

= -11/2

for 1. b) make a diagram and find cosß using sides 1,1,√3

that way you can find a∙b and follow my example of a)

2. In a parallelogram the diagonals bisect each other, but in a rhombus (which is a parallelogram) they bisect each other at right angles.

so take the dot product, and see if you get zero. (you will)

then 1/2 of vector a + 1/2 of vector b will give you a side

etc.

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