The reflection of the point with position vector a- in the plane r-n-q is

The correct option is A a⃗+2 [ ( q⃗ a⃗.n⃗ ) |n⃗ |^2 ]n⃗ P⃗R⃗=r⃗ a⃗ and P⃗Q⃗=2P⃗R⃗=2(r⃗ a⃗) a^1=OQ=OP+PQ a^1=a⃗+2(r⃗ a⃗);r⃗=λn⃗+a⃗ so , ...

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Byju's Answer

Standard XII

Mathematics

Parametric Equation of Normal

The reflectio...

Question

The reflection of the point with position vector $\to a$ in the plane $\to r . \to n = q$ is

\to a + \frac{(\to q - \to a . \to n)}{| \to n |}

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\to a + 2 [\frac{(\to q - \to a . \to n)}{{| \to n |}^{2}}] \to n

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\to a + \frac{2 (\to q + \to a . \to n)}{| \to n |} \to n

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none of these

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Solution

The correct option is A $\to a + 2 [\frac{(\to q - \to a . \to n)}{{| \to n |}^{2}}] \to n$
$\to P R = \to r - \to a$
and $\to P Q = 2 \to P R = 2 (\to r - \to a)$
$^{1} = - - \to O Q = - - \to O P + - - \to P Q$
$^{1} = \to a + 2 (\to r - \to a); \to r = λ \to n + \to a$
so , $(λ \to n + \to a) . \to n = q$
$\Rightarrow\Rightarrow λ = \frac{\to q - \to a . \to n}{(\to n)^{2}}$
so, $^{1} = \to a + 2 [\frac{\to q - \to a . \to n}{{(\to n)}^{2}}] \to n$

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The reflection of the point with position vector →a in the plane →r.→n=q is

The correct option is A →a+2[(→q−→a.→n)|→n|2]→n→PR=→r−→aand →PQ=2→PR=2(→r−→a)→a1=−−→OQ=−−→OP+−−→PQ→a1=→a+2(→r−→a);→r=λ→n+→aso , (λ→n+→a).→n=q⇒⇒λ=→q−→a.→n(→n)2so, →a1=→a+2[→q−→a.→n(→n)2]→n

The reflection of the point with position vector $\to a$ in the plane $\to r . \to n = q$ is