If a- -b- -2k- and c- -2-k- Then altitude of the parallelopiped formed by the vectors a- b- c- having base formed by b- and c- is a- b- c- and a- - b- - c- - are reciprocal system of vectors

Volume of the parallelepiped formed by a⃗ ', b⃗ ', c⃗ ' is 4 ∴ Volume of the parallelepiped formed by a⃗, b⃗, c⃗ is 1/4 b⃗×c⃗=1/4a⃗ ' ∴ | b⃗×c⃗ |=√(2)/4=1/2√( ...

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Standard XI

Mathematics

Applications Scalar Triple Product

If a⃗ '=î+ĵ,b...

Question

If $\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k$ and $\to c^{'} = 2^i +^j -^k$ . Then altitude of the parallelopiped formed by the vectors $\to a, \to b, \to c$ having base formed by $\to b$ and $\to c$ is $(\to a, \to b, \to c$ and ${\to a}^{'}, {\to b}^{'}, {\to c}^{'}$ are reciprocal system of vectors)

1

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

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\frac{1}{\sqrt{6}}

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\frac{1}{\sqrt{2}}

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Solution

The correct option is D $\frac{1}{\sqrt{2}}$
Volume of the parallelepiped formed by $\to a^{'}, \to b^{'}, \to c^{'}$ is 4
$∴$ Volume of the parallelepiped formed by $\to a, \to b, \to c$ is $\frac{1}{4}$
$\to b \times \to c = \frac{1}{4} \to a^{'} ∴ ∣ ∣ \to b \times \to c ∣ ∣ = \frac{\sqrt{2}}{4} = \frac{1}{2 \sqrt{2}}$
$∴$ length of altitude = $\frac{1}{4} \times 2 \sqrt{2} = \frac{1}{\sqrt{2}}$ .

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Similar questions

Q. If

\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

and

\to c^{'} = 2^i +^j -^k

. Then altitude of the parallelopiped formed by the vectors

\to a, \to b, \to c

having base formed by

\to b

and

\to c

(\to a, \to b, \to c

and

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

are reciprocal system of vectors)

Q. If

\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

and

\to c^{'} = 2^i +^j -^k

. Then altitude of the parallelopiped formed by the vectors

\to a, \to b, \to c

having base formed by

\to b

and

\to c

(\to a, \to b, \to c

and

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

are reciprocal system of vectors)

Q. Find the altitude of a parallelopiped determined by

\to a, \to b, \to c

if yhe base

\to a, & \to b

and if

\to a =^i +^j +^k; \to b = 2^i + 4^j -^k & \to c =^i +^j + 3^k

Q. If

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, then the unit vectors parallel to

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Q. If

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

\to c = -^i + 2^j -^k

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If →a ′=^i+^j,→b ′=^i+^j+2^k and →c ′=2^i+^j−^k. Then altitude of the parallelopiped formed by the vectors →a,→b,→c having base formed by →b and →c is (→a,→b,→c and →a′,→b′,→c′ are reciprocal system of vectors)

The correct option is D 1√2Volume of the parallelepiped formed by →a ′,→b ′,→c ′ is 4 ∴ Volume of the parallelepiped formed by →a,→b,→c is 14 →b×→c=14→a ′∴∣∣→b×→c∣∣=√24=12√2 ∴ length of altitude = 14×2√2=1√2.