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Let P(3,2,6) be a point in space and Q b...

Let `P(3,2,6)` be a point in space and `Q` be a point on line ` vec r=( hat i- hat j+2 hat k)+mu(-3 hat i+ hat j+5 hat k)dot` Then the value of `mu` for which the vector ` vec P Q` is parallel to the plane `x-4y+3z=1` is a. 1/4 b. -1/4 c. 1/8 d. -1/8

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Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4 .

If vec p=5 hat i+lambda hat j-3 hat k\ a n d\ vec q= hat i+3 hat j-5 hat k , then find the value of lambda such that vec p+ vec q and vec p- vec q are perpendicular vectors.

If vec p=5 hat i+lambda hat j-3 hat k and vec q= hat i+3 hat j-5 hat k , then find the value of lambda , so that vec p+ vec q and vec p- vec q are perpendicular vectors.

If the planes vec rdot( hat i+ hat j+ hat k)=q_1, vec rdot( hat i+2a hat j+ hat k)=q_2a n d vec rdot(a hat i+a^2 hat j+ hat k)=q_3 intersect in a line, then the value of a is a. 1 b. 1//2 c. 2 d. 0

Determine the shortest distance between the pair of lines : vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d\ vec r=(2 hat i- hat k)+mu(2 hat i+2 hat k)dot

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

If vec a=x hat i+2 hat j-\ z hat k and vec b=3 hat i-\ y hat j+ hat k are two equal vectors, then write the value of x+y+zdot

Find the distance of the point (-1,-5,-10) from the point of intersection of line vec r=2 hat i- hat j+2 hat k+lambda(3 hat i+4 hat j+2 hat k) and the plane vec r ( hat i- hat j+ hat k)=5.

Write the value of p for which vec a=3 hat i+2 hat j+9 hat k\ a n d\ vec b= hat i+p hat j+3 hat k are parallel vectors.

If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d\ vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec c

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