Find the position vector of the mid point of the vector joining the points P(2, 3, 4) andQ(4,1,2).
If a,bandc are three non-zero non-coplanar vectors, then find the linear relation between the following four vectors: a−2b+3c,2a−3b+4c,3a−4b+5c,7a−11b+15⋅
If a,bandc are three non-zero vectors, no two of which ar collinear, a+2b is collinear with c and b+3c is collinear with a, then find the value of ∣∣a+2b+6c∣∣˙
If 4i^+7j^+8k^,2i^+3j^+24and2i^+5j^+7k^ are the position vectors of the vertices A,BandC, respectively, of triangle ABC , then the position vecrtor of the point where the bisector of angle A meets BC is a. 32(−6i^−8j^−k^) b. 32(6i^+8j^+6k^) c. 31(6i^+13j^+18k^) d. 31(5j^+12k^)
Let ABCD be a p[arallelogram whose diagonals intersect at P and let O be the origin. Then prove that OA+OB+OC+OD=4OP˙
Let G1,G2andG3 be the centroids of the triangular faces OBC,OCAandOAB, respectively, of a tetrahedron OABC˙ If V1 denotes the volumes of the tetrahedron OABCandV2 that of the parallelepiped with OG1,OG2andOG3 as three concurrent edges, then prove that 4V1=9V1˙
If a,bandc are non-coplanar vectors, prove that the four points 2a+3b−c,a−2b+3c,3a+ 4b−2canda−6b+6c are coplanar.