With vectors a = 5.5 and b = 4.2, what are (a) the z component of a x b , (b) the z component of a x c , and (c) the z component of b x c ?
The angle between a and b is 90 degrees.
To find the z component of the cross product between two vectors, you need to know the values of their x, y, and z components. In this case, you're given the vectors a = 5.5 and b = 4.2, and the angle between them is 90 degrees.
First, let's find the cross product between a and b. Since the angle between them is 90 degrees, the magnitude of the cross product will be the product of the magnitudes of the two vectors, multiplied by the sine of the angle between them. The direction of the cross product will be perpendicular to both a and b, so it will be either pointing upwards or downwards along the z-axis.
(a) The z component of a x b can be found using the formula: z = |a| * |b| * sin(angle).
Since the magnitude of a is 5.5 and the magnitude of b is 4.2, we can calculate the z component of a x b as follows:
z = 5.5 * 4.2 * sin(90 degrees) = 23.1.
(b) The z component of a x c cannot be determined without knowing the vector c or additional information.
(c) Similarly, the z component of b x c cannot be determined without knowing the vector c or additional information.
Note: If you provide the vector c or additional information, I can help you calculate the z component of a x c and b x c as well.