Find the vector and Cartesian equations of the plane passing through the point with position vector 2hat(i)+6hat(j)+3hat(k)" and normal to the vector "hat(i)+3hat(j)+5hat(k).

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 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 parametric form of vector equation of a line passing through a point (2,-1,3) and parallel to line vec(r)=(hat(i)+hat(j))+t(2hat(i)+hat(j)-2hat(k))

Find the projection of the vector hat i + 3 hat j + 7 hat k on the vector 7 hat i - hat j + 8 hat k .

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

Show that the points whose position vectors are 2hat(i) + 3hat(j) - 5hat(k), 3hat(i) + hat(j) - 2hat(k) and 6hat(i) - 5hat(j) + 7hat(k) are collinear.

Forces of magnitude 5sqrt2 and 10sqrt2 units acting in the directions 3hat(i) + 4hat(j) + 5hat(k) and 10hat(i) + 6hat(j) - 8hat(k) , respectively, act on a particle which is displaced from the point with position vector 4hat(i) - 3hat(j) - 2hat(k) to the point with position vector 6hat(i) + hat(j) - 3 hat(k) . Find the work done by the forces.