Let the vectors aand bbe such that ∣a∣=3and ∣∣b∣∣=32, then a×bis a unit vector, if the angle between aand b
(A) π/6 (B) π/4 (C) π/3 (D) π/2
OABCDE is a regular hexagon of side 2 units in the XY-plane in the first quadrant. O being the origin and OA taken along the x-axis. A point P is taken on a line parallel to the z-axis through the centre of the hexagon at a distance of 3 unit from O in the positive Z direction. Then find vector AP.
If non-zero vectors aandb are equally inclined to coplanar vector c,thenc can be a. ∣a∣+2∣∣b∣∣∣a∣a+∣a∣+∣∣b∣∣∣∣b∣∣b b. ∣a∣+∣∣b∣∣∣∣b∣∣a+∣a∣+∣∣b∣∣∣a∣b c. ∣a∣+2∣∣b∣∣∣a∣a+∣a∣+2∣∣b∣∣∣∣b∣∣b d. 2∣a∣+∣∣b∣∣∣∣b∣∣a+2∣a∣+∣∣b∣∣∣a∣b
Vectors a=i^+2j^+3k^,b=2i^−j^+k^ and c=3i^+j^+4k^, are so placed that the end point of one vector is the starting point of the next vector. Then the vector are (A) not coplanar (B) coplanar but cannot form a triangle (C) coplanar and form a triangle (D) coplanar and can form a right angled triangle
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.
Statement 1: If ∣∣a+b∣∣=∣∣a−b∣∣, then a and b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.