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Karnataka SSLC (Class 10) Vectors & 3D Geometry — practice questions

Explore 55 free Vectors & 3D Geometry questions in Karnataka SSLC (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 55.

The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ isRead the answer and worked solution →The distance of a point $P(x,y)$ from the origin isRead the answer and worked solution →The mid-point of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ isRead the answer and worked solution →The distance between the points $(0,0)$ and $(3,4)$ isRead the answer and worked solution →The distance between the points $(1,2)$ and $(4,6)$ isRead the answer and worked solution →The mid-point of the segment joining $(2,3)$ and $(4,7)$ isRead the answer and worked solution →The distance of the point $(5,12)$ from the origin isRead the answer and worked solution →The point that divides the segment joining $(1,2)$ and $(3,4)$ in the ratio $1:1$ isRead the answer and worked solution →The area of the triangle with vertices $(0,0)$, $(4,0)$ and $(0,3)$ isRead the answer and worked solution →Three points are collinear if the area of the triangle formed by them isRead the answer and worked solution →The distance between the points $(2,3)$ and $(2,8)$ isRead the answer and worked solution →A point that lies on the x-axis has itsRead the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead 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. $(x_2-x_1)^2+(y_2-y_1)^2$
  2. $\sqrt{(x_2-x_1)+(y_2-y_1)}$
  3. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  4. $|x_2-x_1|+|y_2-y_1|$
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Correct answer: C. $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

1. The distance formula comes from the Pythagoras theorem. 2. $PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. 3. The square root is essential; without it the value would be the square of the distance. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch7 'Coordinate Geometry', §7.2_

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

  1. $x+y$
  2. $x^2+y^2$
  3. $\sqrt{x+y}$
  4. $\sqrt{x^2+y^2}$
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Correct answer: D. $\sqrt{x^2+y^2}$

1. The origin is $O(0,0)$. 2. Using the distance formula: $OP=\sqrt{(x-0)^2+(y-0)^2}=\sqrt{x^2+y^2}$. 3. So the distance from the origin is $\sqrt{x^2+y^2}$. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch7 'Coordinate Geometry', §7.2_

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The mid-point of the line 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. $\left(x_1+x_2,\ y_1+y_2\right)$
  3. $\left(\dfrac{x_1-x_2}{2},\ \dfrac{y_1-y_2}{2}\right)$
  4. $\left(x_1 x_2,\ y_1 y_2\right)$
Show answer and solution

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

1. The mid-point divides the segment in the ratio 1:1. 2. Its coordinates are the averages: $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$. 3. This is a special case of the section formula. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch7 'Coordinate Geometry', §7.3_

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