For any two vectors a and b, we always have ∣∣a+b∣∣≤∣a∣+∣∣b∣∣
Let ABC be triangle, the position vecrtors of whose vertices are respectively i^+2j^+4k^ , -2i^+2j^+k^and2i^+4j^−3k^ . Then DeltaABC is a. isosceles b. equilateral c. right angled d. none of these
If the vectors 3p+q;5p−3qand2p+q;4p−2q are pairs of mutually perpendicular vectors, then find the angle between vectors pandq˙
In a triangle ABC,DandE are points on BCandAC, respectivley, such that BD=2DCandAE=3EC˙ Let P be the point of intersection of ADandBE˙ Find BP/PE using the vector method.
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.
ABCD parallelogram, and A1andB1 are the midpoints of sides BCandCD, respectivley . If ∀1+AB1=λAC,thenλ is equal to a. 21 b. 1 c. 23 d. 2 e. 32
If AO+OB=BO+OC , then A,BnadC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these