Question

4 Evaluate
(A+B).(A−B)
if
A=2i−3j+5k
and
B=3i+j−2k
20
22
24
26

Answer 1

Answer on Questionn #56119 – Math – Vector Calculus

Evaluate $(A + B) * (A - B)$ if $A = 2i - 3j + 5k$ and $B = 3i + j - 2k$.

a) 20

b) 22

c) 24

d) 26

Solution

First find $A + B$ and $A - B$

$$A + B = (2i - 3j + 5k) + (3i + j - 2k) = 5i - 2j + 3k$$ $$A - B = (2i - 3j + 5k) - (3i + j - 2k) = -i - 4j + 7k$$

Now, we can find the scalar product (dot product) of these vectors. Remember that for the unit vectors following identity holds $i * i = j * j = k * k = 1$ and $i * j = i * k = j * k = 0$

$$\begin{array}{l} (A + B) * (A - B) = (5i - 2j + 3k) * (-i - 4j + 7k) \\ = -5ii - 20ij + 35ik + 2ij + 8jj - 14jk - 3ik - 12jk + 21kk \\ = -5 + 8 + 21 = 24 \\ \end{array}$$

Answer: c) 24.

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