Vector Multiplication and Angle Determination for d1 and 3d2

[1MileCrash]

Homework Statement

d1 = 4i - 2j + 4k
d2 = -5i + 5j - k

Find

(d1 + d2) * (d1 x 3d2)

Homework Equations

The Attempt at a Solution

My first step was to add d1 and d2, which results in
-i + 3j + 3k

I then multiplied d2 by 3 to get
-15i + 15j - 3k

My problem is multiplying d1 and 3d2. I'm a bit confused on how to get the angle.

I believe the formula for the magnitude is absin(theta), however the angle is something I don't quite understand. It is also my understanding that I use the "Right hand test" to get the direction of C.

I think I can find the magnitudes by squaring i, j, k, then adding them, then taking the square root, so I have a and b. What should I do to determine the angle between d1 and 3d2? I think I've done this before, but lacking a third dimension, so it was just a 2 dimensional triangle.

EDIT: I just read the chapter again and got to a final answer of 0 for this problem. Agree?

Thanks!

 

[Mark44]

Homework Statement

d1 = 4i - 2j + 4k
d2 = -5i + 5j - k

Find

(d1 + d2) * (d1 x 3d2)

Homework Equations

The Attempt at a Solution

My first step was to add d1 and d2, which results in
-i + 3j + 3k

I then multiplied d2 by 3 to get
-15i + 15j - 3k

Both of these look OK.

My problem is multiplying d1 and 3d2. I'm a bit confused on how to get the angle.

Haven't you seen a formula for calculating the cross product using the coordinates of the two vectors. This formula uses something called a pseudo-determinant, with i, j, and k across the top row, and the coordinates for the two vectors in the next two rows.

I believe the formula for the magnitude is absin(theta), however the angle is something I don't quite understand. It is also my understanding that I use the "Right hand test" to get the direction of C.

I think I can find the magnitudes by squaring i, j, k, then adding them, then taking the square root, so I have a and b. What should I do to determine the angle between d1 and 3d2? I think I've done this before, but lacking a third dimension, so it was just a 2 dimensional triangle.

EDIT: I just read the chapter again and got to a final answer of 0 for this problem. Agree?

Thanks!

Yes, I agree.