Find the intercept cut off by the plane `vec(r)=(6hat(i)+4hat(j)-3hat(k))=12` on the coordinate axes.

For the plane vec(r).(2hat(i)+3hat(j)+5hat(k))=3

Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

Find the angle between the line vec(r)=(2hat(i)-hat(j)+hat(k))+t(6hat(i)+2hat(j)-2hat(k))" and the plane "vec(r)*(6hat(i)+3hat(j)+2hat(k))=8

Find the non-parametric form of vector equation, and Cartesian equations of the plane vec(r)=(6hat(i)-hat(j)+hat(k))+s(-hat(i)+2hat(j)+hatk)+t(-5hat(j)-4hat(j)-5hat(k))

The length of the bot^(r) from the origin to plane vec(r).(3hat(i)+4hat(j)+12hat(k))=26 is …………..

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

The coordinates of the point where the line vec(r)=(6i-j-3k)+t(-i+4k)" meets the plane "vec(r)*(hat(i)+hat(j)-hat(k))=3 are

Find the workdone if a particle moves from position vec(r )_(1)=(2hat(j)+hat(j)-3hat(k)) to a position vec(r )_(2)=(4hat(i)+6hat(j)-7hat(k)) under the effect of force vec(F)=(3hat(i)+2hat(j)+4hat(k))N .