For the vectors with a = 3.3 and b = 2.2, what are (a) the z component of AxB, (b) the z component of AxC, and (c) the z component of BxC?
To find the z component of the cross product between two vectors, we need to calculate the determinant of a 3x3 matrix.
The formula for the cross product between two vectors A and B is given by:
A x B = (A2B3 - A3B2)i + (A3B1 - A1B3)j + (A1B2 - A2B1)k
Let's calculate the z component for each cross product.
(a) To find the z component of A x B:
A x B = (A2B3 - A3B2)i + (A3B1 - A1B3)j + (A1B2 - A2B1)k
where A = 3.3 and B = 2.2
Substituting the values:
A x B = (0 - 0)i + (0 - 0)j + (3.3 * 2.2 - 2.2 * 3.3)k
= 0i + 0j - 0.99k
= -0.99k
Therefore, the z component of A x B is -0.99.
(b) To find the z component of A x C:
We need the values of vector C.
(c) To find the z component of B x C:
We need the values of vector C.
Please provide the values of vector C so we can continue with parts (b) and (c).
To find the z component of the cross product between two vectors, we use the formula:
A x B = (A_y * B_z - A_z * B_y)i + (A_z * B_x - A_x * B_z)j + (A_x * B_y - A_y * B_x)k,
where A and B are the given vectors, and i, j, k are the unit vectors along the x, y, and z-axis, respectively.
Now let's calculate the z component of the cross products:
(a) To find the z component of A x B:
Given: A = 3.3, B = 2.2.
Using the formula:
A x B = (0 * 0 - 0 * 0)i + (0 * 2.2 - 3.3 * 0)j + (3.3 * 0 - 0 * 2.2)k
Simplifying:
A x B = 0i + 0j + 0k
The z component of A x B is 0.
(b) To find the z component of A x C:
The value of C is not provided. Please provide the components of vector C to proceed with the calculation.
(c) Similarly, to find the z component of B x C:
The value of C is not provided. Please provide the components of vector C to proceed with the calculation.