Question

If
A=i−2j−3k
,
B=2i+3j+k
and
C=i+3j−2k
, compute
|(A×B)×C|

2(√2)

5(√26)

3(√21)

4(√11)

Answer 1

Answer on Question #56113 – Math – Vector Calculus

If $A = i - 2j - 3k$, $B = 2i + 3j + k$ and $C = i + 3j - 2k$, compute $|(A \times B) \times C|$

2(√2)

5(√26)

3(√21)

4(√11)

Solution

$$A \times B = \begin{bmatrix} i & j & k \\ 1 & -2 & -3 \\ 2 & 3 & 1 \end{bmatrix} = i(-2 * 1 - (-3) * 3) - j(1 * 1 - (-3) * 2) + k(1 * 3 - (-2) * 2) = \\ = i(-2 + 9) - j(1 + 6) + k(3 + 4) = 7i - 7j + 7k.$$ $$(A \times B) \times C = \begin{bmatrix} i & j & k \\ 7 & -7 & 7 \\ 1 & 3 & -2 \end{bmatrix} = i(-7 * (-2) - 7 * 3) - j(7 * (-2) - 7 * 1) + k(7 * 3 - (-7)1) = \\ = i(14 - 21) - j(-14 - 7) + k(21 + 7) = -7i + 21j + 28k.$$ $$|(A \times B) \times C| = \sqrt{(-7)^2 + 21^2 + 28^2} = \sqrt{49 + 441 + 784} = \sqrt{1274} = \sqrt{7 * 7 * 26} = 7\sqrt{26}.$$

Answer: $7\sqrt{26}$.

www.AssignmentExpert.com