(A) Let $\vec{a} = \frac{1}{3} (2\hat{i} - 2\hat{j} + \hat{k})$.First,we check if it is a unit vector by calculating its magnitude:$|\vec{a}| = \sqrt{

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(A) Let $\vec{a} = \frac{1}{3} (2\hat{i} - 2\hat{j} + \hat{k})$.First,we check if it is a unit vector by calculating its magnitude:$|\vec{a}| = \sqrt{(\frac{2}{3})^2 + (-\frac{2}{3})^2 + (\frac{1}{3})^2} = \sqrt{\frac{4}{9} + \frac{4}{9} + \frac{1}{9}} = \sqrt{\frac{9}{9}} = 1$.Since the magnitude is $1$,it is a unit vector.Thus,option $A$ is correct.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

Easy

The vector $\frac{1}{3} (2\hat{i} - 2\hat{j} + \hat{k})$ is ....

A
a unit vector.
B
making an angle of $\pi/3$ with the vector $2\hat{i} - 4\hat{j} + 3\hat{k}$.
C
perpendicular to the vector $3\hat{i} - 2\hat{j} - \hat{k}$.
D
none of these.

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Basic , Modulus and Algebra of vectors

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If three points $A, B, C$ are collinear,whose position vectors are $i - 2j - 8k$,$5i - 2k$,and $11i + 3j + 7k$ respectively,then the ratio in which $B$ divides $AC$ is

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Let $PQRS$ be a quadrilateral. If $M$ and $N$ are midpoints of the sides $PQ$ and $RS$ respectively,then $\overrightarrow{PS} + \overrightarrow{QR} =$

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The vector $\frac{1}{3} (2\hat{i} - 2\hat{j} + \hat{k})$ is ....

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The unit vector parallel to the resultant vector of $2i + 4j - 5k$ and $i + 2j + 3k$ is

The vector in the direction of vector $5 \hat{i} - \hat{j} + 2 \hat{k}$ with a magnitude of $8$ units is:

If $ABCD$ is a parallelogram and the position vectors of $A, B, C$ are $i + 3j + 5k, i + j + k$ and $7i + 7j + 7k$, then the position vector of $D$ will be:

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