Show that (a−b)×(a+b)=2a×b and given a geometrical interpretation of it.
Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.
Let a,b,andcanda′,b′,c′ are reciprocal system of vectors, then prove that a′×b′+b′×c′+c′×a′=[abc]a+b+c .
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.
ABCD is a tetrahedron and O is any point. If the lines joining O to the vrticfes meet the opposite faces at P,Q,RandS, prove that APOP+BQOQ+CROR+DSOS=1.
In triangle ABC,∠A=300,H
is the orthocenter and D
is the midpoint of BC.
is produced to T
such that HD=DT
The length AT
is equal to
(d). none of these