Find the unit vector in the direction of the sum of the vectors, →a=2i^+2j^−5k^and →b=2i^+j^+3k^.
A pyramid with vertex at point P has a regular hexagonal base ABCDEF , Positive vector of points A and B are i^andi^+2j^ The centre of base has the position vector i^+j^+3k^˙ Altitude drawn from P on the base meets the diagonal AD at point G˙ find the all possible position vectors of G˙ It is given that the volume of the pyramid is 63 cubic units and AP is 5 units.
ABC is a triangle and P any point on BC. if PQ is the sum of AP + PB +PC , show that ABPQ is a parallelogram and Q , therefore , is a fixed point.
ABCD is a parallelogram. If LandM are the mid-points of BCandDC respectively, then express ALandAM in terms of ABandAD . Also, prove that AL+AM=23AC˙
The vectors xi^+(x+1)j^+(x+2)k^,(x+3)i^+(x+4)j^+(x+5)k^and(x+6)i^+(x+7)j^+(x+8)k^ are coplanar if x is equal to a. 1 b. −3 c. 4 d. 0
If a=i^+j^+k^,b=4i^+3j^+4k^ and c=i^+αj^+βk^ are linearly dependent vectors & ∣c∣ = 3 , then ordered pair (α,β) is (1,1) (b) (1,−1) (−1,1) (d) (−1,−1)
If the vectors aandb are linearly idependent satisfying (3tanθ+1)a+(3secθ−2)b=0, then the most general values of θ are a. nπ−6π,n∈Z b. 2nπ±611π,n∈Z c. nπ±6π,n∈Z d. 2nπ+611π,n∈Z