If a - 2i-3j-4k- b- i-5j-2k and c- 3i-15j-6k- then evaluate - a-a a-b a-c b-a b-b b-c c-a c-b c-c -

The correct option is D 0We know nbsp; | nbsp;a.a amp; nbsp;a.b amp;a.c nbsp; nbsp;b.a amp; nbsp;b.b amp; b.c nbsp; n ...

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Finding Inverse Using Elementary Transformations

If a = 2i+3...

Question

If $a = 2 i + 3 j + 4 k, b = i + 5 j + 2 k$ and $c = 3 i + 15 j + 6 k,$ then evaluate $∣ ∣ ∣ ∣ \begin{matrix} a . a & a . b & a . c b . a & b . b & b . c c . a & c . b & c . c \end{matrix} ∣ ∣ ∣ ∣ .$

-1

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2 \hat{i} + 3 \hat{j} + 6 \hat{k} and 3 \hat{i} - 6 \hat{j} + 2 \hat{k} .

\vec{a} = 3 \hat{i} + \hat{j} - 4 \hat{k} and \vec{b} = 6 \hat{i} + 5 \hat{j} - 2 \hat{k} .

¯ ¯ ¯ a = 3 ¯ i - 4 ¯ j + 2 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i - ¯ j - 6 ¯ ¯ ¯ k

¯ ¯ c = 5 ¯ i - 5 ¯ j - 4 ¯ ¯ ¯ k

\vec{r} \cdot (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) = 1 and \vec{r} \cdot (- \hat{i} + \hat{j}) = 4

\vec{r} \cdot (2 \hat{i} - \hat{j} + 2 \hat{k}) = 6 and \vec{r} \cdot (3 \hat{i} + 6 \hat{j} - 2 \hat{k}) = 9

\vec{r} \cdot (2 \hat{i} + 3 \hat{j} - 6 \hat{k}) = 5 and \vec{r} \cdot (\hat{i} - 2 \hat{j} + 2 \hat{k}) = 9

¯ ¯ ¯ a = 2 ¯ i + 3 ¯ j + 6 ¯ ¯ ¯ k, ¯ ¯ ¯ b = 3 ¯ i - 6 ¯ j + 2 ¯ ¯ ¯ k, ¯ ¯ ¯ c = 6 ¯ i + 2 ¯ j - 3 ¯ ¯ ¯ k

¯ ¯ ¯ a \times ¯ ¯ ¯ b =

2 ¯ i - 3 ¯ j + 4 ¯ ¯ ¯ k, ¯ i - 2 ¯ j + 3 ¯ ¯ ¯ k

3 ¯ i + ¯ j - 2 ¯ ¯ ¯ k

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