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.`

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))

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

The angle between the lines vec(r)=(hat(i)+2hat(j)-3hat(k))+t(2hat(i)+hat(j)-2hat(k))" and the plane "vec(r)*(hat(i)+hat(j))+4=0 is

Find the parametric form of vector eqution of the straight line passing through (-1,2,1) and paralle to the straight line vec(r)=(2hat(i)+3hat(j)-hat(k))+t(hat(i)-2hat(j)+hat(k)) and lines find the shortest distance between the lines.

Find the angle between the line vec r= hat i+2 hat j- hat k+lambda( hat i- hat j+ hat k) and the plane vec rdot(2 hat i- hat j+ hat k)=4.

If the planes vec(r).(hat(i)+2hat(j)+3hat(k))=7andvec(r).(lambdahat(i)+2hat(j)-7hat(k))=26 are perpendicular. Find the value of lambda.

Find the unit vector perpendicular to the plane vec rdot(2 hat i+ hat j+2 hat k)=5.

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 .

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