Use the cross product to find a vector perpendicular to each of the following pairs.
a) (4,0,0) and (0,0,4)
I plugged in the cross product formula and got (0, -16, 0)
Find two vectors perpendicular to both (3, -6, 3) and (-2, 4, 2).
I found one using the cross product. The one I found was (-24, -12, 0). How would I find another one?
If you reduce your vectors, you can find others with the same property.
eg. your vector [0,-16,0] is -16[0,1,0]
[-24,-12,0] = -12[2,1,0]
any scalar multiple of [2,1,0] will work
To find a vector perpendicular to two given vectors using the cross product, you can follow these steps:
1. Write down the two vectors you want to find a perpendicular vector to. Let's call the vectors A and B:
A = (4, 0, 0)
B = (0, 0, 4)
2. Take the cross product of these two vectors using the formula:
(A x B) = (AyBz - AzBy, AzBx - AxBz, AxBy - AyBx)
3. Substitute the values from the vectors into the formula:
(A x B) = (4 * 0 - 0 * 0, 0 * 4 - 0 * 0, 4 * 0 - 0 * 4)
4. Perform the necessary calculations:
(A x B) = (0, 0, 0 - 0)
5. Simplify the resulting vector:
(A x B) = (0, 0, 0)
The resulting vector (0, 0, 0) represents the zero vector. This means that the given vectors A and B are parallel and do not have a unique vector perpendicular to them.
Therefore, the cross product of (4, 0, 0) and (0, 0, 4) is (0, 0, 0).