If the points (1, 1, lambda) and (-3, 0,...

If the points (1, 1, `lambda`) and (-3, 0, 1) be equidistant from the plane `vecr.(3hati+4hatj-12hatk)+13=0` find the value of `lambda`.

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If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane vecr.(3hati+4hatj-12hatk)+13=0 then find the value of p.

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If the distance of the plane x - y + z + lambda = 0 from the point (1, 1, 1) is d_1 and the distance of this point from the origin is d_2 and d_2d_2 = 5 then find the value of lambda .

Find the equation of the plane passing through (a, b, c) and parallel to the plane vecr.(hati+hatj+hatk)=2 .

Find the distance of the point (-1, -5, -10) from the point of intersection of the line vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk)=5

Find the direction cosines of perpendicular from the origin to the plane vecr.(6hati-3hatj-2hatk)+1=0 .

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Find the direction cosines of the unit vector perpendicular to the plane vecr.(6hati-3hatj-2hatk)+1=0 passing through the origin.

If the points (0, 1, -2), (3, lambda, -1) and (mu, -3, -4) are collinear, verify whether the point (12, 9, 2) is also on the same line.

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK

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