Posted by Yuni on .
if a & b are perpendicular vectors, show that
*how to show it?just multiply it?if yes where does||come from?
does||show that it should be a value?
| | around a number means "magnitude of". You will need to use the following relationships:
a*a = |a|^2
b*b = |b|^2
a*b = 0, because they have said that a and b are perpendicular.
Th "*" operator means "dot product", which I assume you have learned the meaning of. In general, for vectors x and y,
x*y = |x| |y| cos(theta)
where theta is the angle between the two vectors. Thus, in this case,
a*a -a*b + 2b*a -2b*b
|a|^2 - 2|b|^2
Do problem (b) the same way.
math (clarification) -
My first line should have read:
| | around a number VECTOR means magnitude of that vector