Question

$P(-1,-1,-1)$ and $Q(\lambda ,\lambda ,\lambda )$ are two points in the space such that $PQ=\sqrt{48}$, then value(s) of $\lambda$ can be

• A. $3$
• B. $-5$
• C. $4$
• D. $2$

Answer 1

Answer: (A), (B)

The correct options are
A $3$
B $-5$

Distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

Distance between $(-1,-1,-1)$ and $(\lambda ,\lambda ,\lambda )$ is $\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+(z_1-z_2{)}^2}$

Distance between $(-1,-1,-1)$ and $(\lambda ,\lambda ,\lambda )$ is $\sqrt{{(\lambda +1)}^2+{(\lambda +1)}^2+{(\lambda +1)}^2}$

$\sqrt{3\times {(\lambda +1)}^2}=\sqrt{48}=4\sqrt{3}\Rightarrow (\lambda +1)=\pm 4\Rightarrow \lambda =3,-5$