Displacement vector [3, 0 , -2] and [-1,5,2]displacement vector , both measured in meters. Find the components of the cross product of these vectors.
To find the cross product of two vectors, you can use the following formula:
Vector A x Vector B = (Ay * Bz - Az * By) i - (Ax * Bz - Az * Bx) j + (Ax * By - Ay * Bx) k
Given the components of the displacement vectors as (3, 0, -2) and (-1, 5, 2) respectively, let's calculate the cross product.
Ax = 3
Ay = 0
Az = -2
Bx = -1
By = 5
Bz = 2
Now, substitute these values into the formula:
Vector A x Vector B = ((0 * 2) - (-2 * 5)) i - ((3 * 2) - (-2 * -1)) j + ((3 * 5) - (0 * -1)) k
Simplifying further:
Vector A x Vector B = (-10) i - (8) j + (15) k
Therefore, the components of the cross product are:
(-10, -8, 15)