Let a- -2-k- b-2-k- c-2k- be three vectors- A vector in the plane of b- and c- whose projection on a- is of magnitude -23 is

The correct options are B 2î ĵ+5k̂ C 2î+3ĵ 3k̂ r⃗=b⃗+λc⃗=(1+λ )î+(2+λ)ĵ (1+2λ)k̂ Projection of r⃗ on a⃗ is r⃗.a⃗|a⃗|=±√(23)⇒2(1 ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

Let a⃗ =2î-...

Question

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

2^i + 3^j - 3^k

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2^i + 3^j + 3^k

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- 2^i -^j + 5^k

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2^i +^j + 5^k

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Solution

The correct options are
B $- 2^i -^j + 5^k$
C $2^i + 3^j - 3^k$
$\to r = \to b + λ \to c = (1 + λ)^i + (2 + λ)^j - (1 + 2 λ)^k$
Projection of $\to r$ on $\to a$ is
$\frac{\to r . \to a}{| \to a |} = \pm \sqrt{\frac{2}{3}} \Rightarrow \frac{2 (1 + λ) - (2 + λ) - (1 + 2 λ)}{\sqrt{6}} = \pm \sqrt{\frac{2}{3}}$
$\Rightarrow - λ - 1 = \pm 2$
$\Rightarrow λ = 1, - 3$
$\to r = 2^i + 3^j - 3^k, - 2^i -^j + 5^k$

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Similar questions

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Let →a=2^i−^j+^k,→b=^i+2^j−^k,→c=^i+^j−2^k be three vectors. A vector in the plane of →b and →c whose projection on →a is of magnitude √23 is

The correct options are B −2^i−^j+5^k C 2^i+3^j−3^k→r=→b+λ→c=(1+λ)^i+(2+λ)^j−(1+2λ)^kProjection of →r on →a is→r.→a|→a|=±√23⇒2(1+λ)−(2+λ)−(1+2λ)√6=±√23⇒−λ−1=±2⇒λ=1,−3→r=2^i+3^j−3^k,−2^i−^j+5^k

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