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Uttarakhand Board Class 10 Vectors & 3D Geometry — practice questions

Explore 72 free Vectors & 3D Geometry questions in Uttarakhand Board Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vectors & 3D Geometry questions and exercises with answers

Showing questions 1–30 of 72.

The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is:Read the answer and worked solution →The distance of the point $P(x,y)$ from the origin is:Read the answer and worked solution →The midpoint of the segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is:Read the answer and worked solution →The distance between the origin and the point $(3,4)$ is:Read the answer and worked solution →The midpoint of the segment joining $(2,3)$ and $(4,7)$ is:Read the answer and worked solution →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →The y-coordinate of any point lying on the x-axis is:Read the answer and worked solution →The x-coordinate of any point lying on the y-axis is:Read the answer and worked solution →The distance between the points $(a,b)$ and $(-a,-b)$ is:Read the answer and worked solution →The point dividing the segment from $(1,1)$ to $(4,7)$ in the ratio 1:2 is:Read the answer and worked solution →The distance of the point $(-3,4)$ from the origin is:Read the answer and worked solution →The coordinates of the origin are:Read the answer and worked solution →In which quadrant does the point (−4, 7) lie?Read the answer and worked solution →A point lies on the x-axis when:Read the answer and worked solution →What are the coordinates of the origin?Read the answer and worked solution →Which point lies on the y-axis?Read the answer and worked solution →Identify the quadrant of the point (5, −3).Read the answer and worked solution →Find the distance between (1, 2) and (4, 6).Read the answer and worked solution →Find the distance of (3, 4) from the origin.Read the answer and worked solution →Find the distance between (−2, 1) and (3, 5).Read the answer and worked solution →Are the points A(1, 1), B(2, 3), C(3, 5) collinear?Read the answer and worked solution →Determine whether triangle with vertices A(0, 0), B(4, 0), C(0, 3) is right-angled.Read the answer and worked solution →Find x such that the distance from (x, 1) to (2, 3) is √8.Read the answer and worked solution →Find the midpoint of A(2, −3) and B(8, 5).Read the answer and worked solution →Find the point P that divides the segment joining A(1, 2) and B(7, 8) in the ratio 1 : 2.Read the answer and worked solution →The midpoint of segment AB is (4, 5). If A = (2, 3), what is B?Read the answer and worked solution →Find the point dividing the segment joining (4, −1) and (−2, −3) in the ratio 1 : 3.Read the answer and worked solution →The centroid of a triangle with vertices A(1, 1), B(4, 7), C(7, 1) is:Read the answer and worked solution →Point (3, k) is the midpoint of segment joining (1, 4) and (5, 6). Find k.Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →

Worked practice questions

The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is:

  1. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  2. $(x_2-x_1)^2+(y_2-y_1)^2$
  3. $\sqrt{(x_2+x_1)^2+(y_2+y_1)^2}$
  4. $\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}$
Show answer and solution

Correct answer: A. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance formula: √[(x₂−x₁)²+(y₂−y₁)²].

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The distance of the point $P(x,y)$ from the origin is:

  1. $x+y$
  2. $\sqrt{x^2+y^2}$
  3. $x^2+y^2$
  4. $\sqrt{x^2-y^2}$
Show answer and solution

Correct answer: B. $\sqrt{x^2+y^2}$

Distance from origin (0,0) to (x,y) is √(x²+y²).

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The midpoint of the segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is:

  1. $\left(\dfrac{x_1 x_2}{2},\ \dfrac{y_1 y_2}{2}\right)$
  2. $(x_1+x_2,\ y_1+y_2)$
  3. $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$
  4. $\left(\dfrac{x_1-x_2}{2},\ \dfrac{y_1-y_2}{2}\right)$
Show answer and solution

Correct answer: C. $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

Midpoint = average of coordinates: ((x₁+x₂)/2, (y₁+y₂)/2).

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