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Show that the points A(-2 hat i+3 hat j+...

Show that the points `A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k)`and `C(7 hat i- hat k)`are collinear.

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To show that the points \( A(-2 \hat{i} + 3 \hat{j} + 5 \hat{k}), B(\hat{i} + 2 \hat{j} + 3 \hat{k}), C(7 \hat{i} - \hat{k}) \) are collinear, we will find the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{BC} \) and check if one is a scalar multiple of the other. ### Step 1: Find the vector \( \overrightarrow{AB} \) The vector \( \overrightarrow{AB} \) is given by the formula: \[ \overrightarrow{AB} = \overrightarrow{B} - \overrightarrow{A} \] ...
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