Find the distance of the point (-1, -5, ...

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`

A

10

B

11

C

12

D

13

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The correct Answer is:

D

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Show that the line vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr.(hati+2hatj-hatk)=3

Find the distance of a point (2, 5, -3) from the plane vecr.(6hati-3hatj+2hatk)=4

The angle between the line vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+hatk) and the plane barr.(3hati-4hatj-hatk)+5=0 is sin^(-1)((5)/(2sqrt(91))) .

Find the shortest distance between lines vecr=6hati+2hatj+2hatk+lambda (hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk).

Find the angle between the vectors 2hati-hatj+hatk and 3hati+4hatj-hatk .

Find the angle between the vector 2hati-3hatj+hatk and hati+hatj-2hatk .

Find the shortest distance between the lines vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

Find the equation of the plane through the line of intersection of vecr.(2hati-3hatj+4hatk)=1 and vecr.(hati-hatj)+4=0 and perpendicular to vecr.(2hati-hatj+hatk)+8=0

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to X- axis.

Find the shortest distance between the lines vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

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