Guided Example #3 - Vectors

Find the dot product of the vectors A and B.

$A = 2 i + 5 j - 4 k$ and $B = - 2 i - 3 j - 5 k$

a. $- 4 i - 15 j + 20 k$
b. $2 i + 2 j - 9 k$
c. $1$
d. None of the above

The correct answer is C. To see why, view each of the steps below.

By definition: $A • B$ $= (2 i + 5 j - 4 k) • (- 2 i - 3 j - 5 k)$ $= (2 \times - 2) + (5 \times - 3) + (- 4 \times - 5)$ $= - 4 + - 15 + 20$ $= 1$

By definition: $A • B$ $= (2 i + 5 j - 4 k) • (- 2 i - 3 j - 5 k)$ $= (2 \times - 2) + (5 \times - 3) + (- 4 \times - 5)$ $= - 4 + - 15 + 20$ $= 1$