Q. 8

# Show that the line  is parallel to the plane Also, find the distance between them.

Given - and To prove – The line and the plane are parallel &

To find – The distance between them

Direction ratios of the line = (1, 3, 4)

Direction ratios of the normal of the plane = (1, 1, - 1)

Formula to be used – If (a, b, c) be the direction ratios of a line and (a’, b’, c’) be the direction ratios of the normal to the plane, then, the angle between the two is given by The angle between the line and the plane    Hence, the line and the plane are parallel.

Now, the equation of the plane may be written as x + y - z = 7.

Tip – If ax + by + c + d = 0 be a plane and be a line vector, then the distance between them is given by The distance between the plane and the line   units

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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers