Vector Multiplication in a Triangle on the Cartesian Plane

[Lucian09474]

Homework Statement

For the vectors in a Triangle, with a = 16, b = 12, and c = 20 what are

(a) the magnitude and (b) the direction of A x B

(c) the magnitude and (d) the direction of A x C

(e) the magnitude and (f) the direction B x C

this is Vector Multiplication.

Homework Equations

ABsin(ø)
pythagorean theorem
tan^-1 (y/x)
3. The Attempt at a Solution

16i x 12j = 192 (magnitude of A x B it is correct) and the direction is along the -x axis (believed)

since this is vector multiplication, I realized that the best way to do it was using the determinant. which is a value associated with a square matrix. We can get the above relations following matrix algebra procedures to calculate the determinant of a 3×3 matrix, which in favor ends up giving us the vector product. if I am not mistaken the vector product can be expressed by multiplying the vectors, now here is where the problem arises. multiplying vector is not commutative and when multiplying vectors you get a new one (on the Z direction?)

 

[SteamKing]

You should learn the different results of the cross-products between the unit vectors.

A handy mnemonic (a memory device) is

i j k | i j

which translated means (reading from left to right):

i x j = k

j x k = i

k x i = j

if you read the mnemonic in reverse, from right to left, you get:

j x i = -k

i x k = -j

k x j = -i

Any unit vector crossed with itself is zero:

i x i = j x j = k x k = 0

This can be confirmed also by writing out the cross products using determinants.

 

[Lucian09474]

ah Indeed thank you very much. surprise to find out that after all the attempts all of the answers were 192. and the directions were a little bit tricky but I got the right answer.

thanks for the guidance.