# math

posted by .

if a & b are perpendicular vectors, show that
a)(a+2b).(a-b)=|a|^2-2|b|^2
b)(a+b).(a-b)=|a|^2+|b|^2

*how to show it?just multiply it?if yes where does||come from?
does||show that it should be a value?

• math -

| | 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+2b)*(a-b)=
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

## Similar Questions

1. ### Vectors Help me pls!

Dtermine the value of a so that u=2i+aj+k and 4i-2j-2k are perpendicular Did you just start this topic?
2. ### math

Can someone please show us how to show 1500 x 2.1?

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 …
4. ### Math

Given two non-collinear vectors a and b, show that a, axb, and (axb)xa are mutually perpendicular. Also Express the unit vectors i, j, and k as ordered triplets and show that i x j = k what are ordered triplets?
5. ### Physics

Suppose vectors a&b, if a cross b=c. Show that c is perpendicular to a&b.
6. ### Physics

Suppose vectors a&b if a x b=c. Show that c is perpendicular to a&b. Please help me.
7. ### math

Please show me how to solve: For what value of k are the graphs of 12y = -3x + 8 and 6y =kx - 5 parallel?
8. ### maths

Given that vector c and vector d are non zero vectors such that vector c =x1i + y1j + z1k and vector d =(y1z2-y2z1)+(x1y2 -x2y1)show that the two vectors are perpendicular.
9. ### Math

Let a, b, and c be unit vectors, such that a+b+c=0. Show that the angle between any two of these vectors is 120 degrees. I proved this geometrically, but now my teacher wants a proof using vectors, and I don't know what to do.
10. ### Linear Algebra

Please , I donĀ“t know how to do this demonstration: If A and B are mutually perpendicular vectors( different to zero vector) and "c" is any number show that : || A +cB ||>= ||A||

More Similar Questions