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

A vector v in the plane of a and b is v=a+λb v=(î+ĵ+k̂)+λ(î ĵ+k̂) Projection of v on c =1√(3) v.c|c|=1√(3) (1+λ) (1 λ) (1+λ)√(3)=1√(3) (1+λ) (1 λ) (1+λ)=1 λ=2 ...

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Byju's Answer

Standard XIII

Physics

Vectors

Let a=î+ĵ+k̂,...

Question

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

^i - 3^j + 3^k

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- 3^i - 3^j -^k

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3^i -^j + 3^k

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^i + 3^j - 3^k

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Solution

The correct option is C $3^i -^j + 3^k$
A vector $\to v$ in the plane of $\to a$ and $\to b$ is $\to v = \to a + λ \to b$
$⟹ \to v = (^i +^j +^k) + λ (^i -^j +^k)$
Projection of $\to v$ on $\to c$ = $\frac{1}{\sqrt{3}}$
$⟹ \frac{\to v . \to c}{∣ ∣ \to c ∣ ∣} = \frac{1}{\sqrt{3}}$
$⟹ \frac{(1 + λ) - (1 - λ) - (1 + λ)}{\sqrt{3}} = \frac{1}{\sqrt{3}}$
$⟹ (1 + λ) - (1 - λ) - (1 + λ) = 1$
$λ = 2$
So, $\to v = 3^i -^j + 3^k$

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