If vectors 𝐚, 𝐛, 𝐜 are coplanar, then show that |[ 𝐚 b c; 𝐚·𝐚 𝐚·b 𝐚·𝐜; 𝐛·𝐚 ...

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[IIT 1989] If vectors a, b and c are coplanar show that following determinant equals a null vector. [IIT 1989] If vectors a, b and c are coplanar show that following determinant equals a null vector.
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If a, b and c are three non-coplanar vectors such that a+b+c=α d and b+c+d=β a, then a+b+c+d is e... If a, b and c are three non-coplanar vectors such that a+b+c=α d and b+c+d=β a, then a+b+c+d is e...
[IIT 1987] Find the value of 1/(1-a) + 1/(1-b) + 1/(1-c) where ai+j+k, i+bj+k, i+j+ck are coplanar. [IIT 1987] Find the value of 1/(1-a) + 1/(1-b) + 1/(1-c) where ai+j+k, i+bj+k, i+j+ck are coplanar.
Show that the vectors `a-2b+4c,-2a+3b-6c and -b+2c` are coplanar vector, where a,b,c are Show that the vectors `a-2b+4c,-2a+3b-6c and -b+2c` are coplanar vector, where a,b,c are
Show that the following vectors are coplanar.|vector| Show that the following vectors are coplanar.|vector|