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 quadrilateral PQRS,PQ=a,QR,b,SP=a−b,M is the midpoint of QRandX is a point on SM such that SX=54SM˙ Prove that P,XandR are collinear.
If ∣∣a+b∣∣<∣∣a−b∣∣, then the angle between aandb can lie in the interval a. (π/2,π/2) b. (0,π) c. (π/2,3π/2) d. (0,2π)
If the resultant of three forces F1=pi^+3j^−k^,F2=6i^−k^andF3=−5i^+j^+2k^ acting on a parricle has magnitude equal to 5 units, then the value of p is a. −6 b. −4 c. 2 d. 4
Two forces AB and AD are acting at vertex A of a quadrilateral ABCD and two forces CB and CD at C prove that their resultant is given by 4EF , where E and F are the midpoints of AC and BD, respectively.
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
Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.
Let u^=i^+j^,v^=i^−j^andw^=i^+2j^+3k^˙ If n^ is a unit vector such that u^n^˙=0andv^n^˙=0, then find the value of ∣∣w^n^˙∣∣˙