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Question

To show that: ^i^j6^k;^i3^j+4^k;2^i5^j+3^k are coplanar.

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Solution

Let the given vector,

a=^i^j6^kb=^i3^j+4^kc=2^i5^j+3^k

Vector a,b,c are coplanar

if [abc]=0

Now,

[abc]=∣ ∣116134253∣ ∣=1(9+20)+1(38)6(5+6)=1156=1111=0

Hence, the given vectors are coplanar.

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