Compute the following scalar triple products- i-2j-3k - 2i-j-k - j-k

The correct option is C 12 ( i 2j+3k ) ×( 2i+j k ) .( j+k ) =( i( 2 3 ) j( 1 ) 6 ) +( 1 ( 4 ) nbsp;) .( j+k ) =( i+7j+5k ) .( j+k ...

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Addition of Vectors

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Question

Compute the following scalar triple products: $(i - 2 j + 3 k) \times (2 i + j - k) . (j + k)$

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(2 i - 3 j + k) . (i - j + 2 k) \times (2 i + j - k)

[(3 i - 2 j - 2 k) \times (i - k)] \times [(i + j + k) \times (i - 2 j + 3 k)]

V = 2 i + j - k

W = i + 3 k

U

[U V W]

(\vec{r} \cdot \vec{n} = d) :

\vec{r} = (2 \hat{i} - \hat{k}) + λ \hat{i} + μ (\hat{i} - 2 \hat{j} - \hat{k})

\vec{r} = (1 + s - t) \hat{t} + (2 - s) \hat{j} + (3 - 2 s + 2 t) \hat{k}

\vec{r} = (\hat{i} + \hat{j}) + λ (\hat{i} + 2 \hat{j} - \hat{k}) + μ (- \hat{i} + \hat{j} - 2 \hat{k})

\vec{r} = \hat{i} - \hat{j} + λ (\hat{i} + \hat{j} + \hat{k}) + μ (4 \hat{i} - 2 \hat{j} + 3 \hat{k})

¯ ¯ ¯ v = 2 ¯ i + ¯ j - ¯ ¯ ¯ k

¯ ¯¯ ¯ w = ¯ i + 3 ¯ ¯ ¯ k

¯ ¯ ¯ u

[¯ ¯ ¯ u ¯ ¯ ¯ v ¯ ¯¯ ¯ w]

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