Unit - VI Vector

Vector is a physical quantity which has both magnitude and a fixed direction. Also, it satisfies the vector algebra. Here, we have a guide of the solutions related to Vector Geometry.

In Optional Mathematics of Class 10, a 5 marks question from Vector Geometry is fixed and is asked from inside the book. So, you can get those 5 free marks if you can either memorize or understand these vector geometry proofs.

We have few important laws (and formulae) in Vector that are essential for solving questions of Vector Geometry.
  1. Triangle Law: $\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}$
  2. Mid Point Theorem: $\overrightarrow{OM} = \dfrac{ \overrightarrow{OA} + \overrightarrow{OB}}{2}$

Vector Geometry

Exercise 2

Question: $$( \vec{x} + \vec{y} )^ 2 \ = \ ( \vec{x} - \vec{y} )^ 2$$ , prove that $\vec{x}$ and $\vec{y}$ are perpendicular to each other.

Solution:

Given,

$$( \vec{x} + \vec{y})^2 = ( \vec{x} - \vec{y} )^2$$

$$\text{or,} \vec{x}^2 + \vec{y}^2 + 2 \vec{x} \vec{y} = \vec{x}^2 + \vec{y}^2 - 2 \vec{x} \vec{y}$$

$$ \text{or,} 2 \vec{x} \vec{y} = - 2  \vec{x} \vec{y}$$

$$ \text{or,} 4 \vec{x} \vec{y} = 0$$

$$\text{or,} \vec{x} . \vec{y} = 0$$

Here, the dot product of two vectors x and y is zero. Hence, the given vectors are perpendicular.


10) Prove that $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = 0$ in the given triangle ABC. 







About Readmore Optional Mathematics Book 10

Author: D. R. Simkhada
Editor: I. R. Simkhada

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Class 10 - Vector - Vector Geometry Solved Exercises || Readmore Optional Mathematics is a collection of the solutions related to proofs of vector geometry from the vector chapter for Nepal's Secondary Education Examination (SEE) appearing students.

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