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  • If the vector 4i+11j+mk , 7i+2j+6k and i+5j+4k are coplanar , then m is

If the vector 4i+11j+mk , 7i+2j+6k and i+5j+4k are coplanar , then m is

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Solution: As the three vector are coplanar , one will be a linear combination of the other two.

Therefore ,

\ 4i+11j+mk=x(7i+2j+6k)+y(i+5j+4k)\ \Rightarrow 4=7x+y ......(1)\ \Rightarrow 11=2x+5y .........(2)\ \Rightarrow m=6x+4y ...... (3)

From (1) and (2) x=3/11 ;and; y=23/11

Now , from (3)\ m=6 imes 3/11+4 imes 23/11=10

Posted by

Deependra Verma

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