Consider the parallelepiped with sides a -3 -2 -k- b -2 k- and c -3 -3 k- then the angle between a and the plane containingthe face determined by b and c- is A- cos -19-14B- sin -11-3C- sin -19-14D- sin -12-3

The correct option is C sin^ 1(9/14) b⃗×c⃗= 3î ĵ+2k̂ Cos(90^∘ θ)=a⃗,|b⃗×c⃗|/|a⃗||b⃗×c⃗|=9/14 ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Consider the ...

Question

Consider the parallelepiped with sides $\to a = 3^i + 2^j +^k, \to b =^i +^j +^2 k$ and $\to c =^i + 3^j +^3 k$ then the angle between $\to a$ and the plane containing the face determined by $\to b$ and $\to c$ is

s i n^{- 1} (\frac{1}{3})

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c o s^{- 1} (\frac{9}{14})

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s i n^{- 1} (\frac{9}{14})

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s i n^{- 1} (\frac{2}{3})

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Solution

The correct option is C $s i n^{- 1} (\frac{9}{14})$

$\to b \times \to c = - 3^i -^j + 2^k C o s (90^{\circ} - θ) = \frac{\to a, | \to b \times \to c |}{| \to a | | \to b \times \to c |} = \frac{9}{14}$

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Similar questions

Let $\to a =^i +^j +^k, \to b =^i -^j +^k$ and $\to c =^i -^j -^k$ be three vectors. A vector $\to v$ in the plane of
$\to a$ and $\to b$ , whose projection on $\to c$ is $\frac{1}{\sqrt{3}}$ , is given by

Q. Let

\to a =^i +^j +^k

\to b =^i -^j +^k

and

\to c =^i -^j -^k

be three vectors. A vector

\to v

in the plane of

\to a

and

\to b

, whose projection on

\to c

\frac{2}{\sqrt{3}}

, is given by

Q. Let

\to a =^i +^j +^k

\to b =^i -^j +^k

and

\to c =^i -^j -^k

be three vectors. A vector

\to v

in the plane of

\to a

and

\to b

, whose projection on

\to c

\frac{1}{\sqrt{3}}

, is given by

Q. I: If

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

then

\to a + \to b + \to c = 4^i - 4^j

II: If

\to a =^i -^j + 2^k, \to b = 2^i + 3^j +^k, \to c =^i -^k

, then magnitude of

\to a + 2 \to b - 3 \to c

\sqrt{78}

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Consider the parallelepiped with sides →a=3^i+2^j+^k,→b=^i+^j+^2k and →c=^i+3^j+^3k then the angle between →a and the plane containing the face determined by →b and →c is

The correct option is C sin−1(914) →b×→c=−3^i−^j+2^kCos(90∘−θ)=→a,|→b×→c||→a||→b×→c|=914

Consider the parallelepiped with sides $\to a = 3^i + 2^j +^k, \to b =^i +^j +^2 k$ and $\to c =^i + 3^j +^3 k$ then the angle between $\to a$ and the plane containing the face determined by $\to b$ and $\to c$ is

The correct option is C $s i n^{- 1} (\frac{9}{14})$

$\to b \times \to c = - 3^i -^j + 2^k C o s (90^{\circ} - θ) = \frac{\to a, | \to b \times \to c |}{| \to a | | \to b \times \to c |} = \frac{9}{14}$