If the vectors xi^-3j^+7k^ and i^+yj^-zk^ are collinear then the value of (xy^2)/z is equal

Correct answer: (B) (-9)/7. Given, vectors xi^-3j^+7k^ and i^+yj^-zk^ are collinear ∴x/1=(-3)/y=7/(-z)=k ⇒x=k,-3=kyand7=-kz Now, (xy^2)/z=(k-3)/k(-7)/k=9/k(-7)/k=(-9)/7

Q82 / 150 · MHT CET 2019 (Shift 2) · Mathematics

If the vectors $x \hat{i} - 3 \hat{j} + 7 \hat{k}$ and $\hat{i} + y \hat{j} - z \hat{k}$ are collinear then the value of $\frac{x y^{2}}{z}$ is equal

A
$\frac{9}{7}$
Correct answer
B
$\frac{- 9}{7}$
C
$\frac{- 7}{9}$
D
$\frac{7}{9}$

Solution

Given, vectors

x \hat{i} - 3 \hat{j} + 7 \hat{k}

and

\hat{i} + y \hat{j} - z \hat{k}

are collinear

∴ \frac{x}{1} = \frac{- 3}{y} = \frac{7}{- z} = k

\Rightarrow x = k, - 3 = k y a n d 7 = - k z

Now,

\frac{x y^{2}}{z} = \frac{k (- \frac{3}{k})}{(\frac{- 7}{k})} = \frac{\frac{9}{k}}{\frac{- 7}{k}} = \frac{- 9}{7}

Hence, the correct answer is option: 'B'.

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If the vectors xi^-3j^+7k^ and i^+yj^-zk^ are collinear then the value of xy2z is equal

Solution

Relevant Questions

If the vectors $x \hat{i} - 3 \hat{j} + 7 \hat{k}$ and $\hat{i} + y \hat{j} - z \hat{k}$ are collinear then the value of $\frac{x y^{2}}{z}$ is equal