Q. 6 A5.0( 1 Vote )

Prove that the fo

Answer :

Vectors parallel to the same plane, or lie on the same plane are called coplanar vectors

The three vectors are coplanar if one of them is expressible as a linear combination of the other two.


We have been given that, , and .


We can form a relation using these three vectors. Say,





Comparing coefficients of , and , we get


3 = 2x + 7y …(1)


1 = –x – y …(2)


–1 = 7x + 23y …(3)


Solving equations (1) and (2) for x and y.


Equation (1), 2x + 7y = 3


Equation (2), –x – y = 1


Multiply equation (2) by 2.


–x – y = 1 [× 2


–2x – 2y = 2 …(4)


Solving equations (4) and (1), we get



5y = 5



y = 1


Put y = 1 in equation (2), we get


1 = –x – y


1 = –x – (1)


1 = –x – 1


x = –1 – 1


x = –2


Substituting x = –2 and y = 1 in equation (3), we get


–1 = 7x + 23y


Or 7x + 23y = –1


7(–2) + 23(1) = –1


–14 + 23 = –1


9 ≠ –1


, L.H.S ≠ R.H.S


The value of x and y doesn’t satisfy equation (3).


Thus, , and are not coplanar.


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