The scalar product of 5i + j – 3k and 3i – 4j + 7k is....A15B-15C10D-10

To find the scalar product (also known as the dot product) of two vectors, you multiply their corresponding components and then sum the results. Let's denote the vectors as A and B:

A = 5i + j - 3k
B = 3i - 4j + 7k

The dot product A · B is calculated as follows:

1. Multiply the i-components:
   $5 \times 3 = 15$

2. Multiply the j-components:
   $1 \times (-4) = -4$

3. Multiply the k-components:
   $-3 \times 7 = -21$

4. Sum these products:
   $15 + (-4) + (-21) = 15 - 4 - 21 = -10$

So, the scalar product of the vectors A and B is -10.

Therefore, the correct answer is D) -10.