Let a and b be two unit vectors such that a.b=0 For some x,y∈R, let c=xa+yb+(a×b If (∣c∣=2 and the vector c is inclined at same angle α to both a and b then the value of 8cos2α is
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The axes of coordinates are rotated about the z-axis though an angle of π/4
in the anticlockwise direction and the components of a vector are 22,
Prove that the components of the same vector in the original system are -1,5,4.
Four non –zero vectors will always be
a. linearly dependent b. linearly independent
c. either a or b d. none of these
Prove that point i^
from a triangle in space.
Given three non-zero, non-coplanar vectors a,b,and⋅r1=pa+qb+candr2=a+pb+q⋅
If the vectors r1()+2r2and2r1+r2
are collinear, then (P,q)
Show that the points A(1,−2,−8),B(5,0,−2)andC(1,3,7)
are collinear, and find the ratio in which B
are reciprocal system of vectors, then prove that a′×b′+b′×c′+c′×a′=[abc]a+b+c
Statement 1: In DeltaABC,AB+BC+CA=0
Statement 2: If OA=a,OB=b,thenAB=a+b
Let a=i−k,b=xi+j+(1−x)k and c=yi+xj+(1+x−y)k . Then [abc] depends on (A) only x (B) only y (C) Neither x nor y (D) both x and y