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
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.
Statement 1: if three points P,QandR have position vectors a,b,andc , respectively, and 2a+3b−5c=0, then the points P,Q,andR must be collinear. Statement 2: If for three points A,B,andC,AB=λAC, then points A,B,andC must be collinear.
Find the least positive integral value of x for which the angel between vectors a=xi^−3j^−k^ and b=2xi^+xj^−k^ is acute.
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
Four non –zero vectors will always be a. linearly dependent b. linearly independent c. either a or b d. none of these