Find the angle between two vectors →aand →bwith magnitudes 1 and 2 respectively and when →a→˙b=1.
If i^−3j^+5k^ bisects the angle between a^and−i^+2j^+2k^,wherea^ is a unit vector, then a. a^=1051(41i^+88j^−40k^) b. a^=1051(41i^+88j^+40k^) c. a^=1051(−41i^+88j^−40k^) d. a^=1051(41i^−88j^−40k^)
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
If A,B,C,D are four distinct point in space such that AB is not perpendicular to CD and satisfies ABC˙D=k(∣∣AD∣∣2+∣∣BC∣∣2−∣∣AC∣∣2−∣∣BD∣∣2), then find the value of k˙
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.