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.
If AO+OB=BO+OC , then A,BnadC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these
If α+β+γ=aδandβ+γ+δ=bα,αandδ are non-colliner, then α+β+γ+δ equals a. aα b. bδ c. 0 d. (a+b)γ
If a,b,andc are three non-coplanar non-zero vecrtors, then prove that (a.a)b×c+(a.b)c×a+(a.c)a×b=[bca]a
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
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˙