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  • Provide Solution For R .D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 11 Maths Textbook Solution.

Provide Solution For  R .D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 11 Maths Textbook Solution.

Answers (1)

Answer: \vec{0}

Hint: You must know the rules of vector functions

Given: If G is denotes the centroid of ?ABC , then write the value of \vec{GA}+\vec{GB}+\vec{GC}

Solution: Let \vec{a},\vec{b},\vec{c}be the position vectors of the vertices A, B and C respectively.

Then, the position of centroid G is \frac{\vec{a}+\vec{b}+\vec{c}}{3}

Thus,

\begin{aligned} \overrightarrow{G A}+\overrightarrow{G B}+\overrightarrow{G C} &=\vec{a}-\left(\frac{\vec{a}+\vec{b}+\vec{c}}{3}\right)+\vec{b}-\left(\frac{\vec{a}+\vec{b}+\vec{c}}{3}\right)+\vec{c}-\left(\frac{\vec{a}+\vec{b}+\vec{c}}{3}\right) \\ & \Rightarrow(\vec{a}+\vec{b}+\vec{c})-3\left(\frac{\vec{a}+\vec{b}+\vec{c}}{3}\right) \\ & \Rightarrow(\vec{a}+\vec{b}+\vec{c})-(\vec{a}+\vec{b}+\vec{c}) \\ & \Rightarrow \overrightarrow{0} \end{aligned}

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