Let a-k- b-k- and c-k- be three vectors- A vector v- in the plane of a- and b- - whose projection on c- is 1-3 - is given by -

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 = 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)}

Q. Compute the magnitude of the following vectors:

\to a =^i +^j +^k; \to b = 2^i - 7^j - 3^k; \to c = \frac{1}{\sqrt{3}}^i + \frac{1}{\sqrt{3}}^j - \frac{1}{\sqrt{3}}^k

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Let →a=^i+^j+^k,→b=^i−^j+^k and →c=^i−^j−^k be three vectors. A vector →v in the plane of →a and →b , whose projection on →c is 1√3 , is given by ;

The correct option is D 3^i−^j+3^kLet →v=λ→a+μ→b⇒→v=(λ+μ)^i+(λ−μ)^j+(λ+μ)^kProjection of →v on →c=→v.→c∣∣→c∣∣=1√3⇒(λ+μ)−(λ−μ)−(λ+μ)√3=1√3⇒μ−λ=1or μ=λ+1⇒→v=(2λ+1)^i−^j+(2λ+1)^kFor λ=1,→v=3^i−^j+3^k

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 $;$