Home
Class 12
MATHS
If a and b are two non collinear vectors...

If a and b are two non collinear vectors; then every vector r coplanar with a and b can be expressed in one and only one way as a linear combination: xa+yb=0.

A

(a)x=0, but y is not necessarily zero

B

(b)y=0, but x is not necessarily zero

C

(c)x=0,y=0

D

(d)none of these

Text Solution

Verified by Experts

The correct Answer is:
C
If a and b are two non-zero, non-collinear vectors and x and y are two scalars such that xa+yb=0 then x=0 and y=0 because one will be a scalar multiple off the other and hence collinear which is a contradiction.
Promotional Banner

Similar Questions

Explore conceptually related problems

If a and b are two non-zero and non-collinear vectors then a+b and a-b are

a and b are non-collinear vectors. If c=(x-2) a+b and d=(2x+1)a-b are collinear vectors, then find the value of x.

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

Let vec a and vec b be two non collinear unit vectors. If vec u = vec a - (vec a . vec b) vec b and vec nu = vec a xx vec b , then |vec nu| =

In a four-dimensional space where unit vectors along the axes are hati,hatj,hatk and hatl, and a_(1),a_(2),a_(3),a_(4) are four non-zero vectors such that no vector can be expressed as a linear combination of other (lamda-1) (a_(1)-a_(2))+mu(a_(2)+a_(3))+gamma(a_(3)+a_(4)-2a_(2))+a_(3)+deltaa_(4)=0 , then

If vec alpha and vec beta are two vectors such atht veca. vecb =0 and veca xx vec b =vec0, then:

If vec a, vec b, vec c non zero coplanar vectors, then, [2 vec a - vec b 3 vec b - vec c 4 vec c - vec a] =

Let vec a, vec b and vec c be three non zero vectors such that no two of these are collinear. If the vector vec a + 2 vec b is collinear with vec c and vec b + 3 vec c is collinear with vec a then vec a + 2 vec b + 6 vec c =

If vecx and vecy are two non-collinear vectors and ABC is a triangle with side lengths a, b and c satisfying (20a - 15b) vecx + ( 15b - 12c) vecy+ (12c - 20 a) (vecx xx vecy) = vec0 , then triangle ABC is