NIMCET 2008 Question Paper with solutions

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Question : 29 of 120

Marks: +1, -0

The value of

λ

such that the four points whose position vectors are

3 i-2 j+λ k, 6 i+3 j+k, 5 i+7 j+3 k

and

2 i+2 j+6 k

are coplanar is

-6
4
5
8

Solution:

Let given four points are

A, B, C, D

which are coplanar, if

[ {AB}, {BC}, {CD}]=0

{AB}=3 {i}+5 {j}+(1-λ) {k}

{BC}=- {i}+4 {j}+2 {k}

{CD}=-3 {i}-5 {j}+3 {k}

⇒|\table 3 , 5 , 1-λ ; -1 , 4 , 2 ; -3 , -5 , 3|=0

3(12+10)-5(-3+6)+(1-λ)(5+12)=0

⇒ λ=4

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