Question

Find the cross product →A×→C for:

a) →A=2.0ˆi−4.0ˆj+ˆk and →C=3.0ˆi+4.0ˆj+10.0ˆk
b) →A=3.0ˆi+4.0ˆj+10.0ˆk and →C=2.0ˆi−4.0ˆj+ˆk
c) →A=−3.0ˆi−4.0ˆj and →C=−3.0ˆi+4.0ˆj
d) →C=−2.0ˆi+3.0ˆj+2.0ˆk and →A=−9.0ˆj

Answer 1

The cross product of two vectors can be found using the formula →A × →C = (AyCz - AzCy)⁢ẁ + (AzCx - AxCz)⁢ṿ + (AxCy - AyCx)⁢. Calculate the cross products for the given vectors to find the final results.

Step-by-step explanation:

To find the cross product of two vectors →A and →C, we can use the formula →A × →C = (AyCz - AzCy)⁢ẁ + (AzCx - AxCz)⁢ṿ + (AxCy - AyCx)⁢. Let's calculate the cross products for the given vectors:

a) →A = 2.0i - 4.0j + ⁵k and →C = 3.0i + 4.0j + 10.0k:

→A × →C = (4.010.0 - ⁵4.04.0)⁢⁵i + (⁵2.010.0 - 2.03.0)⁢ṿj + (2.04.0 - ↎4.03.0)⁢Ṻk

= 20.0⁵i - 14.0ṿj - 22.0Ṻk

b) →A = 3.0i + 4.0j + 10.0k and →C = 2.0i - 4.0j + ⁵k:

→A × →C = (⁵4.0⁵-10.0 - ⁵10.0-4.0)⁢⁵i + (10.02.0 - 3.0⁵2.0)⁢ṿj + (3.0-4.0 - 2.0(-4.0))⁢Ṻk

= ⁵80.0⁵i + 2.0ṿj - 2.0Ṻk

c) →A = ↎3.0i - 4.0j and →C = ↎3.0i + 4.0j:

→A × →C = (↎4.0(4.0) - ↎3.0(-3.0))⁢⁵i + (↎3.0(-3.0) - ↎(-3.0)4.0)⁢ṿk

= ↎7.0⁵i + 0ṿj + ↎3.0Ṻk

d) →A = ↎9.0ṿ and →C = -2.0i + 3.0j + 2.0k:

→A × →C = (-2.0Ṻ(-9.0) - (-2.00))(0)i + (2.0ẁ(-9.0) - 3.0Ṻ(-2.0))ṿj + (-3.0ẁ0 - 2.0(-2.0))Ṻk

= 18.0⁢i + 39.0ṿj - 2.0Ṻk