Calculating Unit Vectors and Angles

[andrew.c]

Homework Statement

Given a=2i+3j+k, b=i+2j+k, c=-i-j+k, calculate;

a)unit vectors b^{^} and c^{^} in the directions of b and c respectively.
b)the angle between a and c

Homework Equations

n/a

The Attempt at a Solution

I don't understand a) at all,
but b is just a simple dot product question.


Any ideas for a) ?

 

[rock.freak667]

Do you know what a unit vector is?

 

[Mark44]

a) For any vector x other than the zero vector 0i + 0j + 0k, the vector 1/|x| * x will be a unit vector with the same direction as x.

b) You didn't ask, but one definition of the dot product of vectors a and b is $$a \cdot b = |a||b]| cos \theta$$
where $$\theta$$ is the angle between the two vectors.

 

[andrew.c]

Thank you both. Tbh, I'm still not entirely sure what a unit vector is though, but I do understand Mark44's formula for calculating. Ta

 

[Mark44]

A unit vector has a magnitude (or length) of 1 unit. You can normalize any nonzero vector by shrinking it or lengthening it to a vector with the same direction, and magnitude 1.