Show that if the position vectors of 3 points are (a) -2i+3j+5k , I+2j+3k and 7i-k (b) i-2j+3k , 2i+3j-4k and -7i+4k then the points are collinear.

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- 2 \hat{i} + 3 \hat{j}, \hat{i} + 2 \hat{j} + 3 \hat{k} and 7 \hat{i} - \hat{k}

\to i + \to 2 j + \to 3 k

\to i - \to 2 j + \to 5 k

\to 3 j - \to 4 k

- \to 2 i + \to 3 j - \to 3 k

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

i + 2 j + 3 k

- 2 i + 3 j + 5 k

7 i - k

5 ˆ i + 5 ˆ k, 2 ˆ i + ˆ j + 3 ˆ k

- 4 ˆ i + 3 ˆ j - ˆ k

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