NDA 2024 Maths · Mathematics · Vector Algebra · easy

Three mutually perpendicular vectors vec a, vec b, vec c have magnitudes 1, 2 and 2 respectively. The magnitude of vec a+vec b+vec c is

Single correct option

Three mutually perpendicular vectors

\vec a

\vec b

\vec c

have magnitudes

1

2

and

2

respectively. The magnitude of

\vec a+\vec b+\vec c

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Answer: (A) $3$

Because the vectors are mutually perpendicular, all cross terms vanish:

|\vec a+\vec b+\vec c|^2=1+4+4=9

, so the magnitude is

3

. Trap: 5 adds the magnitudes (valid only for parallel vectors), 9 is the square of the answer, and

\sqrt5

drops one of the two equal terms.

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