Show, by vector methods, that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.
For given vector, a = 2i^ j +2k^ and b = -i^ +j^ - k^ , find the unit vector in the direction of the vector a +b .
Vectors a=−4i^+3k^;b=14i^+2j^−5k^ are laid off from one point. Vector d^ , which is being laid of from the same point dividing the angle between vectors aandb in equal halves and having the magnitude 6, is a. i^+j^+2k^ b. i^−j^+2k^ c. i^+j^−2k^ d. 2i^−j^−2k^
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.
a,b,c are three coplanar unit vectors such that a+b+c=0. If three vectors p,q,andr are parallel to a,b,andc, respectively, and have integral but different magnitudes, then among the following options, ∣p+q+r∣ can take a value equal to a. 1 b. 0 c. 3 d. 2