Question

Given three vectors
a⃗ =−i⃗ −4j⃗ +2k⃗
,
b⃗ =3i⃗ +2j⃗ −2k⃗
,
c⃗ =2i⃗ −3j⃗ +k⃗
, calculate
a⃗ ⋅(b⃗ ×c⃗ )

−6
6
9

−9

Answer 1

Question

Given three vectors $a = -i - 4j + 2k$, $b = 3i + 2j - 2k$, $c = 2i - 3j + k$, calculate a *($b \times c$)

a.-6

b.6

c.9

d.-9

Solution

$$a = (-1; -4; 2); \quad b = (3; 2; -2); \quad c = (2; -3; 1); \quad (a^*[b \times c]) - ?$$

Firstly we find $[b \times c]$

$$\begin{array}{l} [b \times c] = \left( \begin{array}{ccc} i & j & k \\ 3 & 2 & -2 \\ 2 & -3 & 1 \end{array} \right) \\ = i(2 * 1 - (-3) * (-2)) + j(2 * (-2) - 3 * 1) + k(3 * (-3) - 2 * 2) \end{array}$$ $$[b \times c] = -4i - 5j - 5k;$$ $$(a^*[b \times c]) = -1 * (-4) + (-4) * (-5) + 2 * (-5) = 14$$

Answer: $(a^*[b \times c]) = 14$. We don't have correct answer in given multiple choice answers.

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