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) Options: A . &nbsp 1 B . &nbsp 3 √ 2 2 C . &nbsp 1 √ 6 D . &nbsp 1 √ 2

Answer: Option D : D Volume of the parallelepiped formed by → a ′ , → b ′ , → c ′ is 4 ∴ Volume of the parallelepiped formed by → a , → b , → c is 1 4 → b × → c = 1 4 → a ′ ∴ ∣ ∣ → b × → c ∣ ∣ = √ 2 4 = 1 2 √ 2 ∴ length of altitude = 1 4 × 2 √ 2 = 1 √ 2 .

If →a ′=^i+^j,→b ′=^i+^j+2^k and →

Discussion Forum : Vector Algebra

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)

Options:

A .

1

B .

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

C .

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

D .

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

Answer: Option D
:
D
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

\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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Discussion Forum : Vector Algebra

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