Find a unit vector perpendicular to each of the vector a+band a−b where a=3i^+2j^+2k^ and b=i^+2j^−2k^
For given vector, a = 2i^ j +2k^ and b = -i^ +j^ - k^ , find the unit vector in the direction of the vector a +b .
A,B,CandD have position vectors a,b,candd, respectively, such that a−b=2(d−c)˙ Then a. ABandCD bisect each other b. BDandAC bisect each other c. ABandCD trisect each other d. BDandAC trisect each other
Three coinitial vectors of magnitudes a, 2a and 3a meet at a point and their directions are along the diagonals if three adjacent faces if a cube. Determined their resultant R. Also prove that the sum of the three vectors determinate by the diagonals of three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube.
If α+β+γ=aδandβ+γ+δ=bα,αandδ are non-colliner, then α+β+γ+δ equals a. aα b. bδ c. 0 d. (a+b)γ
In a trapezium, vector BC=αAD˙ We will then find that p=AC+BD is collinear withAD˙ If p=μAD, then which of the following is true? a. μ=α+2 b. μ+α=2 c. α=μ+1 d. μ=α+1
Points A(a),B(b),C(c)andD(d) are relates as xa+yb+zc+wd=0 and x+y+z+w=0,wherex,y,z,andw are scalars (sum of any two of x,y,znadw is not zero). Prove that if A,B,CandD are concylic, then ∣xy∣∣∣a−b∣∣2=∣wz∣∣∣c−d∣∣2˙