Question

Evaluate
|(A+B).(A−B)|
if
A=2i−3j+5k
and
B=3i+j−2k

√24

√240

√530

√525

Answer 1

Answer on Question #56112– Math – Vector Calculus

Given that $A = 2i - 3j + 5k$, $B = 3i + j - 2k$

Find $|(A + B) \cdot (A - B)|$

Solution

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

The Dot product formula:

$$a \cdot b = a_x b_x + a_y b_y + a_z b_z$$

Then

$$(A + B) \cdot (A - B) = 5 \cdot (-1) - 2 \cdot (-4) + 3 \cdot 7 = 24$$ $$|(A + B) \cdot (A - B)| = (A + B) \cdot (A - B) = 24$$

Answer:

$$|(A + B) \cdot (A - B)| = 24$$

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