Find the unit vector in the direction of vector PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.
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˙
Let A(t)=f1(t)i^+f2(t)j^andB(t)=g(t)i^+g2(t)j^,t∈[0,1],f1,f2,g1g2 are continuous functions. If A(t)andB(t) are non-zero vectors for all tandA(0)=2i^+3j^,A(1)=6i^+2j^,B(0)=3i^+2i^andB(1)=2j^+6j^ Then,show that A(t)andB(t) are parallel for some t.
The vector a has the components 2p and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angel about the origin in the counterclockwise sense. If, with respect to a new system, a has components (p+1)and1 , then p is equal to a. −4 b. −1/3 c. 1 d. 2
The points with position vectors 60i+3j,40i−8j,ai−52j are collinear if a. a=−40 b. a=40 c. a=20 d. none of these
Vectors a=i^+2j^+3k^,b=2i^−j^+k^ and c=3i^+j^+4k^, are so placed that the end point of one vector is the starting point of the next vector. Then the vector are (A) not coplanar (B) coplanar but cannot form a triangle (C) coplanar and form a triangle (D) coplanar and can form a right angled triangle