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Condition for Coplanarity of Four Points

If the vector...

Question

If the vector area of the triangle whose adjacent sides are $2 \to i + 3 \to j$ and $- 2 i + 4 \to j$ is $λ^k,$ then the value of $λ$ is

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Solution

Let for a $△ A B C$
$A B = 2 \to i + 3 \to j, B C = - 2 \to i + 4 \to j$
$\Rightarrow$ Area of triangle $A B C = \frac{1}{2} (- - \to A B \times - - \to B C) = \frac{(2 \to i + 3 \to j) \times (- 2 \to i + 4 \to j)}{2} = 7^k$

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Condition for Coplanarity of Four Points

Standard XII Mathematics

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