NCERT Class 11 Mathematics — What is the distance between

Q: What is the distance between the two points P(1, 2, 3) and Q(-1, -2, -3)?

The distance formula between two points $(x1, y1, z1)$ and $(x2, y2, z2)$ is $\sqrt{(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2}$. Substituting values: $\sqrt{(-1-1)^2 + (-2-2)^2 + (-3-3)^2} = \sqrt{(-2)^2 + (-4)^2 + (-6)^2} = \sqrt{4 + 16 + 36} = \sqrt{56} = 2\sqrt{14}$.

NCERT · Class 11 · Mathematics · Introduction to Three Dimensional GeometryWhat is the distance between the two points P(1, 2, 3) and Q(-1, -2, -3)?

Step-by-Step Solution

The distance formula between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$. Substituting values: $\sqrt{(-1-1)^2 + (-2-2)^2 + (-3-3)^2} = \sqrt{(-2)^2 + (-4)^2 + (-6)^2} = \sqrt{4 + 16 + 36} = \sqrt{56} = 2\sqrt{14}$.

Detailed Options Breakdown

Option : $2\sqrt{14}$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 1: $\sqrt{14}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Three Dimensional Geometry.

Option 2: $14$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Three Dimensional Geometry.

Option 3: $4\sqrt{7}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Three Dimensional Geometry.

💡 Study Guide: This question tests core syllabus concepts from Introduction to Three Dimensional Geometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Three Dimensional Geometry Revision Notes.

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