Home
Class 12
MATHS
Theorem 1: If a and b are two non collin...

Theorem 1: 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.

A

x=0, but y is not necessarily zero

B

y=0, bu tx is not necessarily zero

C

x=0,y=0

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

Consider the lines L_1 : r=a+lambdab and L_2 : r=b+mua , where a and b are non zero and non collinear vectors. Statement-I L_1 and L_2 are coplanar and the plane containing these lines passes through origin. Statement-II (a-b)cdot(atimesb)=0 and the plane containing L_1 and L_2 is [r a b]=0 which passe through origin.

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

If a,b and c are non-coplanar vectors, then prove that the four points 2a+3b-c,a-2b+3c,3a+4b-2c and a-6b+6c are coplanar.

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

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a( lamda being some non-zero scalar), then a+2b+6c is equal to

If a,b,c are three non-coplanar vectors, then 3a-7b-4c,3a-2b+c and a+b+lamdac will be coplanar, if lamda is

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 a,b and c are non-coplanar vectors and lamda is a real number, then the vectors a+2b+3c,lamdab+muc and (2lamda-1)c are coplanar when

Let a,b,c are three vectors of which every pair is non-collinear, if the vectors a+b and b+c are collinear with c annd a respectively, then find a+b+c.