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

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)$\\ m=6\times 3/11+4\times 23/11=10$

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