Show that the vector i^+j^+k^is equally inclined to the axes OX, OY and OZ.
Find the vector of magnitude 3, bisecting the angle between the vectors a=2i^+j^−k^ and b=i^−2j^+k^˙
If a,b are two non-collinear vectors, prove that the points with position vectors a+b,a−b and a+λb are collinear for all real values of λ˙
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
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 four points 6i^−7j^,16i^−19j^−4k^,3j^−6k^and2i^+5j^+105^ form a tetrahedron in space.
Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l1,m1,n1andl2,m2,n2 are proportional to l1+l2,m1+m2,n1+n2˙ Statement 2: The angle between the two intersection lines having direction cosines as l1,m1,n1andl2,m2,n2 is given by cosθ=l1l2+m1m2+n1n2˙