Question

a particle move one unit northward then 5 unit eastward and then move one unit upward the displacement of the particle from its original position is

(1).7 unit
(2).4unit

$(3).3 \sqrt{3}$
$(4).4 \sqrt{2}$
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Answer 1

answer : option (3) 3√3 unit

explanation : This can be solved easily with help of vector method.

A particle moves one unit northward.i.e., $\vec{OA}=1\hat{j}$

after that particle moves 5 unit eastward .i.e., $\vec{AB}=5\hat{i}$

and then moves one unit upward.i.e., $\vec{BC}=1\hat{k}$

now we have to find displacement of particle from its original position.

I.e., $\vec{OC}$ = ?

we know, $\vec{OC}=\vec{OA}+\vec{AB}+\vec{BC}$

or, $\vec{OC}=1\hat{i}+5\hat{j}+1\hat{k}$

then, magnitude of displacement, |OC| = √{1² + 5² + 1²} = √27 = 3√3 unit.

hence, option (3) is correct choice.