Let a-b-c-d are such that a-b-c-d-0-Let p1 and p2 be the planes determined by the pairs of vectors a-b and c-d respectively - The angle between the planes p1 and p2 is

The correct option is B 0 The plane p_1 contains the vectors a and b into normal is along a×b The normal to plane p_2 is alon ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Planes

Let a,b,c,d...

Question

Let $\to a, \to b, \to c, \to d$ are such that $(\to a \times \to b) \times (\to c \times \to d) = 0$ .Let $p_{1}$ and $p_{2}$ be the planes determined by the pairs of vectors $\to a, \to b$ and $\to c, \to d$ respectively . The angle between the planes $p_{1}$ and $p_{2}$ is

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Solution

The correct option is B $0$
The plane $p_{1}$ contains the vectors $\to a$ and $\to b$ into normal is along $\to a \times \to b$
The normal to plane $p_{2}$ is along $\to c \times \to d$ .
$(\to a \times \to b) \times (\to c \times \to d) = 0$
$\Rightarrow$ two normals are parallel
$∴$ the angle between the planes is zero

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Let →a,→b,→c,→d are such that (→a×→b)×(→c×→d)=0.Let p1 and p2 be the planes determined by the pairs of vectors →a,→b and →c,→d respectively . The angle between the planes p1 and p2 is

The correct option is B 0The plane p1 contains the vectors →a and →b into normal is along →a×→bThe normal to plane p2 is along →c×→d.(→a×→b)×(→c×→d)=0⇒ two normals are parallel∴ the angle between the planes is zero

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