If d- is a non-zero such that d-a- - d-b- - d-c- - 0- The value of - - a- b- c- - is

d⃗.a⃗ = d⃗.b⃗ = d⃗.c⃗ = 0 d⃗ is perpendicular to a⃗, b⃗, c⃗ #160;one of the possibilities is [ b⃗ = λ _1a⃗; c⃗ = λ _2a⃗ ] Then [ [ ...

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Standard XII

Mathematics

Properties of Determinants

If d⃗ is a ...

Question

If $\to d$ is a non-zero such that $\to d . \to a = \to d . \to b = \to d . \to c = 0$ . The value of $[\begin{matrix} \to a & \to b & \to c \end{matrix}]$ is

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Solution

$\to d . \to a = \to d . \to b = \to d . \to c = 0$
$\to d$ is perpendicular to $\to a, \to b, \to c$
one of the possibilities is
$\begin{matrix} \to b = λ_{1} \to a \to c = λ_{2} \to a \end{matrix}$
Then $[\begin{matrix} \to a & \to b & \to c \end{matrix}] = \to a . (\to b \times \to c)$
$\begin{matrix} = \to a . (λ_{1} \to a \times λ_{2} \to a) = \to a . (0) = 0 \end{matrix}$

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If →d is a non-zero such that →d.→a=→d.→b=→d.→c=0. The value of [→a→b→c] is

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