Find $(3 A - 2 B) .$ If $A = (2 i + 3 j - k)$ and $B = (2 i - 5 j + 2 k) .$

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Solution

$3 ¯ ¯¯ ¯ A = 6 \land i + 9 \land j - 3 \land k$
$2 ¯ ¯¯ ¯ B = 4 \land i - 10 \land j + 4 \land k$
$⟹ 3 ¯ ¯¯ ¯ A - 2 ¯ ¯¯ ¯ B = 2 \land i + 19 \land j - 7 \land k$

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Similar questions

If \vec{a} = 3 \hat{i} - \hat{j} - 2 \hat{k} and \vec{b} = 2 \hat{i} + 3 \hat{j} + \hat{k}, find (\vec{a} + 2 \vec{b}) \times (2 \vec{a} - \vec{b}) .

¯ ¯ ¯ a = 3 ¯ i - ¯ j - 2 ¯ ¯ ¯ k

¯ ¯ b = 2 ¯ i + 3 ¯ j + ¯ ¯ ¯ k

(¯ ¯ ¯ a + 2 ¯ ¯ b) \times (2 ¯ ¯ ¯ a - ¯ ¯ b) =

a = 2 i + 3 j + 4 k, b = i + 5 j + 2 k

c = 3 i + 15 j + 6 k,

∣ ∣ ∣ ∣ \begin{matrix} a . a & a . b & a . c b . a & b . b & b . c c . a & c . b & c . c \end{matrix} ∣ ∣ ∣ ∣ .

\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} and \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}

\vec{A} \times \vec{B}

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