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# Find the distance of the point (–1, –5, –10), from the point of intersection of the line and the plane Given, the equation of the line is – The cartesian form of the equation is – x = 3λ + 2 …(1)

y = 4λ – 1 …(2)

and z = 2λ + 2 …(3)

Given equation of plane is – The cartesian form of above equation is –

x – y + z = 5 …(4)

At the point of intersection of line and the plane-

We have –

3λ +2 – (4λ – 1) + (2λ + 2) = 5

λ + 5 = 5

λ = 0

Hence, x = 2 ; y = -1 and z = 2

position vector of the intersection point is or coordinate is (2,-1,2)

By distance formula, we know that distance between two points (x1,y1,z1) and (x2,y2,z2) is given by – distance between (-1, -5, -10) and (2,-1, 2) is given by – D = = 13 units.

Hence, a distance of the point (–1, –5, –10), from the point of intersection of the line and the plane is 13 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