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If the planes vec rdot( hat i+ hat j+ h...

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`

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Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.

Show that the following planes are at right angle: vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.

Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=5\ a n d\ vec rdot(( hat i-2 hat j+2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

Find vec adot vec b when: vec a= hat i-2 hat j+ hat k\ a n d\ vec b=4 hat i-4 hat j+7 hat k

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Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

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