Let the vectors a,b,cbe given as a1i^+a2j^+a3k^,b1i^+b2j^+b3k^,c1i^+c2j^+c3k^. Then show that a×(b+c)=a×b+a×c
Let AandB be two non-parallel unit vectors in a plane. If (αA+B) bisects the internal angle between AandB, then find the value of α˙
If a,b,andc be three non-coplanar vector and aprime,bprimeandc′ constitute the reciprocal system of vectors, then prove that r=(ra˙′)a+(rb˙′)b+(rc˙′)c r=(ra˙′)a′+(rb˙′)b′+(rc˙′)c′
If AndB are two vectors and k any scalar quantity greater than zero, then prove that ∣∣A+B∣∣2≤(1+k)∣∣A∣∣2+(1+k1)∣∣B∣∣2˙
If a,bandc are non-coplanar vectors, prove that the four points 2a+3b−c,a−2b+3c,3a+ 4b−2canda−6b+6c are coplanar.
ABCD parallelogram, and A1andB1 are the midpoints of sides BCandCD, respectivley . If ∀1+AB1=λAC,thenλ is equal to a. 21 b. 1 c. 23 d. 2 e. 32
Find the vector of magnitude 3, bisecting the angle between the vectors a=2i^+j^−k^ and b=i^−2j^+k^˙
If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.