If the position vectors of the point A and B are `3hat(i)+hat(j)+2hat(k) and hat(i)-2hat(j)-4hat(k)` respectively. Then the eqaution of the plane through B and perpendicular to AB is

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

Find the unit vector perpendicular to both 2hat(i) + 3hat(j)+ hat(k) and hat(i)-hat(j)+ 4hat(k)

The position vector of the points P and Q are 5 hat i+7 hat j-2 hat k and -3 hat i+3 hat j+6 hat k , respectively. Vector vec A=3 hat i- hat j+ hat k passes through point P and vector vec B=-3 hat i+2 hat j+4 hat k passes through point Q . A third vector 2 hat i+7 hat j-5 hat k intersects vectors A and Bdot Find the position vectors of points of intersection.

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

If points A,B and C with position vectors 2 hat(i) - hat(j) + hat(k) , hat(i) - 3 hat(j) - 5hat(k) and alpha hat(i) - 3 hat(j) + hat(k) respectively are the vertices of a right-anged triangle with /_C = ( pi )/( 2) , then the values of alpha are

A vector of magnitude 5 and perpendicular to hat(i) - 2 hat(j) + hat(k) and 2 hat(i) + hat(j) - 3 hat(k) is

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

Projection of the vector 2hat(i) + 3hat(j) + 2hat(k) on the vector hat(i) - 2hat(j) + 3hat(k) is :

Find the dot product of two vectors vec(A)=3hat(i)+2hat(j)-4hat(k) and vec(B)=2hat(i)-3hat(j)-6hat(k) .

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.