NDA 2024 Maths · Mathematics · Vector Algebra · medium

If vec a=hat i+λhat j+2hat k and vec b=3hat i-hat j+hat k have equal magnitudes, then λ equals

Single correct option

\vec a=\hat i+\lambda\hat j+2\hat k

and

\vec b=3\hat i-\hat j+\hat k

have equal magnitudes, then

\lambda

equals

Show answer and solution

Answer: (B) $\pm\sqrt6$

|\vec a|^2=1+\lambda^2+4=5+\lambda^2

and

|\vec b|^2=9+1+1=11

. Equal magnitudes give

\lambda^2=6

, so

\lambda=\pm\sqrt6

. Trap:

\pm\sqrt{11}

forgets the contribution

5

of the other components, and

\pm6

forgets to take the square root.

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