If vector a - 2-3-6k- and vector b -2-2-k- then ratio of projection of a on vector b to projection of b on a is equal to

|a| = √(2^2 + 3^2 + 6^2 ) = √(49) = 7 |b| = √(2^2 + 2^2 + 1^2) nbsp; = √(9) = 3 From the condition the ratio will be equal to Ratio = a·b| b| b. a | a | ⋯ ( ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

If vector a =...

Question

If vector $\to a = 2^i - 3^j + 6^k$ and vector $\to b = - 2^i + 2^j -^k$ , then ratio of projection of $\to a$ on vector $\to b$ to projection of $\to b$ on $\to a$ is equal to

\frac{3}{7}

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\frac{7}{3}

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3

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7

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Solution

The correct option is B $\frac{7}{3}$
$| \to a | = \sqrt{2^{2} + 3^{2} + 6^{2}} = \sqrt{49} = 7$
$| \to b | = \sqrt{2^{2} + 2^{2} + 1^{2}} = \sqrt{9} = 3$
From the condition the ratio will be equal to
Ratio $= \frac{\frac{\to a \cdot \to b}{∣ ∣ ∣ \to b ∣ ∣ ∣}}{\frac{\to b . \to a}{∣ ∣ \to a ∣ ∣}} \dots (i)$
Since we know, dot product is commutative $\to a . \to b = \to b . \to a$
Putting in equation $(i),$ we have
Ratio $= \frac{| \to a |}{| \to b |} = \frac{7}{3}$

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If vector →a=2^i−3^j+6^k and vector →b=−2^i+2^j−^k, then ratio of projection of →a on vector →b to projection of →b on →a is equal to

If vector $\to a = 2^i - 3^j + 6^k$ and vector $\to b = - 2^i + 2^j -^k$ , then ratio of projection of $\to a$ on vector $\to b$ to projection of $\to b$ on $\to a$ is equal to