The points `hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k)` are equidistant from the plane `rcdot(5hat(i)+2hat(j)-7hat(k))+9=0`, then they are

The position vectors of points a and b are hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) respectively. The equation of plane is rcdot(5hat(i)+2hat(j)-7hat(k))+9=0 . The points a and b

Show that the points hat i- hat j+3 hat ka n d3( hat i+ hat j+ hat k) are equidistant from the plane vec rdot(5 hat i+2 hat j+ hat k)+9=0 and lie on opposite sides of it.

Show that the vectors 2hat(i)-hat(j)+hat(k) and hat(i)-3hat(j)-5hat(k) are at right angles.

The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-hat(j)+4hat(k)) and the plane rcdot(hat(i)+5hat(j)+hat(k))=5, is

The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-hat(j)+4hat(k)) and the plane rcdot(hat(i)+5hat(j)+hat(k))=5, is

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

If vector hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3 hat(j) - a hat(k) are equal vectors, then the value of a is :

Forces 2hat(i)+hat(j), 2hat(i)-3hat(j)+6hat(k) and hat(i)+2hat(j)-hat(k) act at a point P, with position vector 4hat(i)-3hat(j)-hat(k) . Find the moment of the resultant of these force about the point Q whose position vector is 6hat(i)+hat(j)-3hat(k) .

Find the planes passing through the intersection of plane rcdot(2hat(i)-3hat(j)+4hat(k))=1 and rcdot(hat(i)-hat(j))+4=0 and perpendicular to planes rcdot(2hat(i)-hat(j)+hat(k))=-8

The vector equation of the plane through the point hat(i)+2hat(j)-hat(k) and perpendicular to the line of intersection of the plane rcdot(3hat(i)-hat(j)+hat(k))=1 and rcdot(hat(i)+4hat(j)-2hat(k))=2 , is