Find ∣∣a−b∣∣,if two vector aand bare such that ∣a∣=2,∣∣b∣∣=3and ab˙=4.
If A(−4,0,3)andB(14,2,−5), then which one of the following points lie on the bisector of the angle between OAandOB(O is the origin of reference )? a. (2,2,4) b. (2,11,5) c. (−3,−3,−6) d. (1,1,2)
Let a,b,c be distinct non-negative numbers and the vectors ai^+aj^+ck^,i^+k^,ci^+cj^+bk^ lie in a plane, and then prove that the quadratic equation ax2+2cx+b=0 has equal roots.
Prove that the necessary and sufficient condition for any four points in three-dimensional space to be coplanar is that there exists a liner relation connecting their position vectors such that the algebraic sum of the coefficients (not all zero) in it is zero.
Statement 1:Let A(a),B(b)andC(c) be three points such that a=2i^+k^,b=3i^−j^+3k^andc=−i^+7j^−5k^˙ Then OABC is a tetrahedron. Statement 2: Let A(a),B(b)andC(c) be three points such that vectors a,bandc are non-coplanar. Then OABC is a tetrahedron where O is the origin.
Two forces AB and AD are acting at vertex A of a quadrilateral ABCD and two forces CB and CD at C prove that their resultant is given by 4EF , where E and F are the midpoints of AC and BD, respectively.