Given two vectors a-2-3-6k- b-2-2-1k- and - - ratio of the projection of a on b and the projection of b on a- then the value of - is

The correct option is B 73 Projection of b⃗ on a⃗ will be #160; =bcosθ =a⃗.b⃗a ...(i)Similarly #160;Projection of a⃗ on ...

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Standard XII

Mathematics

Applications of Dot Product

Given two vec...

Question

Given two vectors $a = 2^i - 3^j + 6^k$ , $b = - 2^i + 2^j - 1^k$ and $λ$ = ratio of the projection of $a$ on $b$ and the projection of $b$ on $a,$ then the value of $λ$ is

\frac{3}{7}

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\frac{7}{3}

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Solution

The correct option is B $\frac{7}{3}$
Projection of $\to b$ on $\to a$ will be
$= b c o s θ$
$= \frac{\to a . \to b}{a}$ ...(i)
Similarly
Projection of $\to a$ on $\to b$ will be
$= a c o s θ$
$= \frac{\to a . \to b}{b}$ ...(ii)
Therefore
$λ = \frac{i i}{i}$

$= \frac{\frac{\to a . \to b}{b}}{\frac{\to a . \to b}{a}}$

$= \frac{a}{b}$

$= \frac{\sqrt{2^{2} + 3^{2} + 6^{2}}}{\sqrt{2^{2} + 2^{2} + 1^{2}}}$

$= \frac{\sqrt{49}}{\sqrt{9}}$

$= \frac{7}{3}$

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Similar questions

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Given two vectors a=2^i−3^j+6^k, b=−2^i+2^j−1^k and λ = ratio of the projection of a on b and the projection of b on a, then the value of λ is

The correct option is B 73Projection of →b on →a will be =bcosθ=→a.→ba ...(i)Similarly Projection of →a on →b will be =acosθ=→a.→bb ...(ii)Therefore λ=iii=→a.→bb→a.→ba=ab=√22+32+62√22+22+12=√49√9=73

Given two vectors $a = 2^i - 3^j + 6^k$ , $b = - 2^i + 2^j - 1^k$ and $λ$ = ratio of the projection of $a$ on $b$ and the projection of $b$ on $a,$ then the value of $λ$ is