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Find the vector equation of a line passi...

Find the vector equation of a line passing through the point with position vector `2hat(i) + hat(j) - hat(k)` and parallel to the line joining the points - `hat(i) + hat(j) + 4 hat(k)` and ` hat(i) + 2 hat(j) + 2 hat(k)`.

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The correct Answer is:
` bar r = ( 2 hati + hatj - hatk ) + lamda ( 2 hati + hatj - 2 hatk ) `
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(i) Find the vector equation of a line passing through a point with position vector 2 hat(i) - hat(j) + hat(k) and parallel to the line joining the points with position vectors - hat(i) + 4 hat(j) + hat(k) and hat(i) + 2 hat(j) + 2 hat(k). Also, find the cartesian equivalent of the equation. (ii) Find the vector equation of a line passing through the point with position vector hat(i) - 2 hat(j) - 3 hat(k) and parallel to the line joining the points with position vectors hat(i) - hat(j) + 4 hat(k) and 2 hat(i) + hat(j) + 2 hat(k) . Also, find the cartesian form of the equation.

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