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Linear Combination of Vectors

Let a⃗=2î-ĵ...

Question

Let $\to a = 2^i -^j +^k, \to b =^i + 2^j -^k$ and $\to c =^i +^j - 2^k$ be three vectors. A vector in the plane of $\to b$ and $\to c$ whose projection on $\to a$ is of magnitude $\sqrt{(2 / 3)}$ is

A

2^i + 3^j - 3^k

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B

2^i + 3^j + 3^k

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C

- 2^i -^j + 5^k

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D

2^i +^j + 5^k

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Solution

The correct options are
A $2^i + 3^j - 3^k$
C $- 2^i -^j + 5^k$

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Similar questions

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

be three vectors. A vector in the plane of

\to b

\to c

whose projection on

\to a

is of magnitude

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

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

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

\to r = l \to a + m \to b + n \to c

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

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

be three vectors. A vector

\to v

in the plane of

\to a

\to b

, whose projection on

\to c

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

;

Q. The three vectors

\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k

\to C = 2^i -^j + 4^k

\to a = 2^i + 4^j - 5^k, \to b =^i +^j +^k, \to c =^j + 2^k

, then the unit vectors parallel to

\to a + \to b + \to c

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