If `P-=(1,5,4) and Q-=(4,1,-2)` find the direction ratios of `vec(PQ)`

P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(3,-2,-1), then find the projection length of vec PQ and vec R Sdot

P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection length of vec P Qon vec R Sdot

P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection length of vec P Qon vec R Sdot

If P(-1,2) and Q(3,-7) are two points, express the vectors vec(PQ) in terms of unit vectors hatiand hatj . Also find the distance between points P and Q. What is the unit vector in the direction of vec(PQ) ? Verify that magnitude of unit vector indeed unity.

If vec(OP)=2hati+3hatj-hatk and vec(OQ)=5hati+4hatj-3hatk . Find vec(PQ) and the direction cosines of vec(PQ) .

The resultant vector of vec(P) and vec(Q) is vec(R ) . On reversing the direction of vec(Q) the resultant vector becomes vec(S) . Show that R^(2)+S^(2)=2(P^(2)+Q^(2))

If vec(OP)=2hati+3hatj-hatk and vec(OQ)=3hati-4hatj+2hatk find the modulus and direction cosines of vec(PQ) .

A line is drawn from the point P(1,1,1)and perpendicular to a line with direction ratios, (1,1,1) to intersect the plane x+2y+3z=4 at Q. The locus of point Q is

A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) with directions ratios 2,1,3 passes through the point B(5,3,4). A line L_(3) with direction ratios 2,-2,-1 intersects L_(1) and L_(3) at C and D, resectively. The volume of parallelopiped formed by vec(AB), vec(AC) and vec(AD) is equal to

A charge Q located at a point vec r is in equilibrium under the combined field of three charges q_(1), q_(2) and q_(3) . If the charges q_(1) and q_(2) are located at point vec r_(1) and vec r_(2) respectively, find the direction of the force on Q due to q_(3) in terms of q_(1),(q_2), vec r_(1) vec r_(2) , and vec(r) .