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UPSC NDA I 2023 Mathematics Solved Paper

Question Numbers: 69-70

Consider the following for the next two (02) items that follow :

The position vectors of two points A and B are î - ĵ and ĵ + k̂ respectively.

Question : 70 of 120

Marks: +1, -0

\vec{AB}

Solution:

Concept:

Magnitude of a vector

\vec{v} = x\hat{i} + y\hat{j} + z\hat{k}

|\vec{v}| = \sqrt{x^2 + y^2 + z^2}

Explanation:

Given: Position vector of A is

\vec{OA} = \hat{i} - \hat{j}

Position vector of B is

\vec{OB} = \hat{j} + \hat{k}

We find

\vec{AB} = \vec{OB} - \vec{OA}

\vec{AB} = (\hat{j} + \hat{k}) - (\hat{i} - \hat{j}) = -\hat{i} + 2\hat{j} + \hat{k}

Now compute magnitude:

|\vec{AB}| = \sqrt{(-1)^2 + (2)^2 + (1)^2} = \sqrt{1 + 4 + 1} = \sqrt{6}

Answer:

\sqrt{6}

(Option C).

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