Let D,EandF be the middle points of the sides BC,CAandAB, respectively of a triangle ABC˙ Then prove that AD+BE+CF=0 .
If D,EandF are three points on the sides BC,CAandAB, respectively, of a triangle ABC such that the CDBD,AECE,BFAF=−1
If b is a vector whose initial point divides thejoin of 5i^and5j^ in the ratio k:1 and whose terminal point is the origin and ∣∣b∣∣≤37,thenk lies in the interval a. [−6,−1/6] b. (−∞,−6]∪[−1/6,∞) c. [0,6] d. none of these
The position vector of the points PandQ are 5i^+7j^−2k^ and −3i^+3j^+6k^ , respectively. Vector A=3i^−j^+k^ passes through point P and vector B=−3i^+2j^+4k^ passes through point Q . A third vector 2i^+7j^−5k^ intersects vectors AandB˙ Find the position vectors of points of intersection.
If the projections of vector a on x -, y - and z -axes are 2, 1 and 2 units ,respectively, find the angle at which vector a is inclined to the z -axis.
Show that the point A,B and C with position vectors a =3i^ - 4j^ -4k^ = 2i^ j + k^ and c = i^ - 3j^ - 5k^ , respectively from the vertices of a right angled triangle.