Answer: 56
Step-by-step explanation:
To find the dot product of two vectors A and B (written as A · B), we multiply the corresponding components of each vector and then sum up the results. Given the vectors A and B:
A = 10i + 12j - 8k
B = 8i - 10j - 12k
To calculate the dot product A · B, we follow the formula:
A · B = (A_x * B_x) + (A_y * B_y) + (A_z * B_z)
Where A_x, A_y, and A_z are the components of vector A, and B_x, B_y, and B_z are the components of vector B.
Now, we can plug in the values of A and B:
A · B = (10 * 8) + (12 * (-10)) + (-8 * (-12))
A · B = 80 - 120 + 96
A · B = 56
The dot product of the vectors A and B is 56.