If a- and c- are perpendicular vectors then any vectors b- the vectors a- b-c- and a-b-c- are

The correct option is A perpendicularGiven, a⃗ and c̅ are perpendicular vector then, a×c⃗=1 or a⃗·c⃗=0 a⃗×(b⃗×c⃗) ⇒(a⃗·c⃗) b⃗ (a⃗· b) ...

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Byju's Answer

Standard XII

Mathematics

Definition of Sets

If a⃗ and ...

Question

If $\to a$ and $\to c$ are perpendicular vectors then any vectors $\to b$ , the vectors $\to a \times (\to b \times \to c)$ and $(\to a \times \to b) \times \to c$ are

perpendicular

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parallel

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each equal to 0

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parallel respectively to

\to a

and

\to b

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Solution

The correct option is A perpendicular
Given, $\to a$ and $¯ c$ are perpendicular vector

$then, \to a \times \to c = 1 or \to a \cdot \to c = 0$
$\to a \times (\to b \times \to c)$
$\Rightarrow (\to a \cdot \to c) \to b - (\to a \cdot b) \to c$
$\Rightarrow - (\to a \cdot \to b) \to c \dots (i) ∵ \to a \cdot \to c = 0$
now, $(\to a \times \to b) \times \to C$
$\Rightarrow (\to c \cdot \to a) \to b - (\to b \cdot \to c) \to a$
$- (\to b \cdot \to c) \to a \dots (i i) ∵ \to a \cdot \to c = 0$
Now, doing dot produt of vector in equation (i) and (ii), We get,
$\to a \times (¯ b \times \to c) \cdot (¯ a \times ¯ b) \cdot \to c = (¯ a \cdot \to b) (\to b \cdot \to c) \to c \cdot \to a$
Both vectors are perpendicular
option $A =$ perpendicular

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If →a and →c are perpendicular vectors then any vectors →b, the vectors →a×(→b×→c) and (→a×→b)×→c are

If $\to a$ and $\to c$ are perpendicular vectors then any vectors $\to b$ , the vectors $\to a \times (\to b \times \to c)$ and $(\to a \times \to b) \times \to c$ are