Parallel and perpendicular vectors with given magnitude

[demv18]

Homework Statement

Given two vectors A=9i+1j+9k and B=12i-12j+10k find:
a) Their dot product AB
b) Their cross product AxB
c)The angle between the vectors A and B
d) a vector C that is parallel with A and has the same magnitude as B
e) A vector C that is perpendicular to A and has the same magnitude as B

Homework Equations

dot product: AB=AxBx+AyBy+AzBz

The Attempt at a Solution

I got a, b, and c.
a) (9)(12)+(1)(-12)+(9)(10)=186
b) 118i+18j-96k
c) 42 deg.
d and e) I have no idea how to get the vector to be parallel or perpendicular to A with the same magnitude as B. Just want a simple explanation please!

 

[gneill]

Homework Statement

Given two vectors A=9i+1j+9k and B=12i-12j+10k find:
a) Their dot product AB
b) Their cross product AxB
c)The angle between the vectors A and B
d) a vector C that is parallel with A and has the same magnitude as B
e) A vector C that is perpendicular to A and has the same magnitude as B

Homework Equations

dot product: AB=AxBx+AyBy+AzBz

The Attempt at a Solution

I got a, b, and c.
a) (9)(12)+(1)(-12)+(9)(10)=186
b) 118i+18j-96k
c) 42 deg.
d and e) I have no idea how to get the vector to be parallel or perpendicular to A with the same magnitude as B. Just want a simple explanation please!

A parallel vector will simply lie along the same vector. So a scaled version of the vector will do.

For a perpendicular vector, what is the property of the cross product concerning the direction of the resulting vector?

Sometimes it's handy to find unit vectors in the desired directions and then multiply the unit vector by the desired magnitude. Do you know how to find a unit vector in the same direction as a given vector?