If either a=0and b=0then a×b=0. Is Is the converse true? Justify your answer with an example.
Statement 1: a=3i+pj+3k and b=2i+3j+qk are parallel vectors if p=9/2andq=2. Statement 2: if a=a1i+a2j+a3kandb=b1i+b2j+b3k are parallel, then b1a1=b2a2=b3a3˙
Find the values of λ such that x,y,z=(0,0,0)and(i^+j^+3k^)x+(3i^−3j^+k^)y+(−4i^+5j^)z=λ(xi^+yj^+zk^), where i^,j^,k^ are unit vector along coordinate axes.
In a trapezium, vector BC=αAD˙ We will then find that p=AC+BD is collinear withAD˙ If p=μAD, then which of the following is true? a. μ=α+2 b. μ+α=2 c. α=μ+1 d. μ=α+1
If aandb are two unit vectors and θ is the angle between them, then the unit vector along the angular bisector of a and b will be given by a. cos(θ/2)a−b b. 2cos(θ/2)a+b c. 2cos(θ/2)a−b d. none of these
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˙
Show that the vectors 2a−b+3c,a+b−2canda+b−3c are non-coplanar vectors (where a,b,c are non-coplanar vectors)