Question

Let vectors A = (2,-1,1), B(3, 0, 5), and C = (1,4,-2), where (x, y, z) are the components of the vectors along i, j, k and respectively. Calculate the following:

A.B = ____

Answer 1

The scalar product of vectors A and B, given as A = (2, -1, 1) and B = (3, 0, 5), is calculated using the dot product formula and equals 11.

Step-by-step explanation:

The student asked to calculate the scalar product, also known as the dot product, of vectors A and B. To find the scalar product A.B, use the formula:

A.B = Ax Bx + Ay By + Az Bz.

For vectors A = (2, -1, 1) and B = (3, 0, 5), the calculation is as follows:

A.B = (2)(3) + (-1)(0) + (1)(5) = 6 + 0 + 5 = 11.

To calculate the dot product (also known as the scalar product) of two vectors A and B, we multiply the corresponding components of the vectors and then add up the results. In this case, we have vector A = (2,-1,1) and vector B = (3,0,5). So the dot product is: A.B = (2)(3) + (-1)(0) + (1)(5) = 6 + 0 + 5 = 11.

Therefore, the scalar product A.B equals 11.