Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:
The position vector of the co-ordinates \(\log_{10}1,\log_{10}10,\log_{10}100\) with respect to the origin will be
Options:

\[\hat{i} + 10\hat{j} + 100\hat{k}\]

\[ -\hat{i} +- 10\hat{j} - 100\hat{k}\]

\[\hat{i} - 10\hat{j} + 100\hat{k}\]

\[ \hat{j} + 2\hat{k}\]

Correct Answer:

\[ \hat{j} + 2\hat{k}\]

Explanation:
\(\begin{aligned}\text{The position vector for coordinates } &(x,y,z)\text{ is } x\hat{i} + y\hat{j} + z\hat{k}.\text{ So, required position vector is }\\ &\log_{10}1\hat{i}+\log_{10}10\hat{j}+\log_{10}100\hat{k}\\ &0+\hat{j}+2\log_{10}10\hat{k}\\ &\hat{j}+2\hat{k}\end{aligned}\)