If a- b- c- are non-zero- non-collinear vectors such that a vector p- - -a-b-cos 2- - a-b-c- and a vector q- - -a-c-cos - - a-c-b- then p- - q- is

The correct option is D Perpendicular to a⃗ Given #160; p⃗= | a⃗ | | b⃗ |cos (2π (a⃗∧b⃗))c⃗ p⃗=(a⃗×b)c⃗ q⃗= | a⃗ | | c⃗ |cos (π (a⃗∧c⃗))b⃗ ...

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Applications of Dot Product

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c$ are non-zero, non-collinear vectors such that a vector
$\to p = | a | | b | cos (2 π - (\to a \land \to b)) \to c$ and $a$ vector $\to q = | a | | c | cos (π - (\to a \land \to c)) \to b$ then $\to p + \to q$ is

Parallel to

\to a

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Perpendicular to

\to a

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Coplanar with

\to b

and

\to c

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Coplanar with

\to a

and

\to c

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\to a, \to b, \to c

\to p, \to q, \to r

\to p = \frac{\to b \times \to c}{[\begin{matrix} \to b & \to c & \to a \end{matrix}]}

\to q = \frac{\to c \times \to a}{[\begin{matrix} \to c & \to a & \to b \end{matrix}]}

\to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

(\to a + \to b) . \to p + (\to b + \to c) . \to q + (\to c + \to a) . \to r

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

¯ ¯ ¯ p, ¯ ¯ ¯ q, ¯ ¯ ¯ r

\to p = \frac{\to b \times \to c}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}, \to q = \frac{\to c \times \to a}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}, \to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

(\to a + \to b + \to c) . (\to p + \to q + \to r)

\to a, \to b, \to c

\to p, \to q, \to r

(\to a \times \to p) + (\to b \times \to q) + (\to c \times \to r)

\to a, \to b, \to c

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}

\to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

\to a, \to b, \to c

{\to a \times (\to b + \to c)} \times {\to b \times (\to c - \to a)}

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