If vectors a 1 → = x i ^ - j ^ + k ^ and a 2 → = i ^ + y j ^ + z k ^ are collinear, then a possible unit vector parallel to the vector x i ^ + y j ^ + z k ^ is:

a → 1 and a → 2 are collinear So, x 1 = - 1 y = 1 z Unit vector in direction of x i ^ + y j ^ + z k ^ = ± 1 3 i ^ - j ^ + k ^

Mathematics - Vector Question with Solution | TestHub

MathematicsVectorGeneral definitions, Angle between vectors, Section formula, Geometrical resultsEasy2 minPYQ_2021

MathematicsEasysingle choice

If vectors $\vec{a_{1}} = x \hat{i} - \hat{j} + \hat{k}$ and $\vec{a_{2}} = \hat{i} + y \hat{j} + z \hat{k}$ are collinear, then a possible unit vector parallel to the vector $x \hat{i} + y \hat{j} + z \hat{k}$ is:

Options:

Answer:

Solution:

${\vec{a}}_{1}$ and ${\vec{a}}_{2}$ are collinear

So, $\frac{x}{1} = \frac{- 1}{y} = \frac{1}{z}$

Unit vector in direction of

$x \hat{i} + y \hat{j} + z \hat{k} = \pm \frac{1}{\sqrt{3}} (\hat{i} - \hat{j} + \hat{k})$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:General definitions, Angle between vectors, Section formula, Geometrical results

⏱ 2mℹ️ Source: PYQ_2021

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