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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Exercise 23 .1 Question 25 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot  Products  Exercise 23 .1 Question 25 Maths Textbook Solution.

Answers (1)

Answer:  Proved

Hint:  You must know the rules of solving vectors.

Given:  If  A, B and C have position vectors \left ( 0,1,1, \right ) \left ( 3,1,5 \right ) and \left ( 0,3,3 \right ) respectively. Show \Delta ABCright angled at C.

Solution: Given that,

\begin{aligned} &\overrightarrow{O A}=0 \hat{\imath}+\hat{\jmath}+\hat{k} \\ &\overrightarrow{O B}=3 \hat{\imath}+1 \hat{\jmath}+5 \hat{k} \\ &\overrightarrow{O C}=0 \hat{\imath}+3 \hat{\jmath}+3 \hat{k} \\ \end{aligned}

\begin{aligned} &\overrightarrow{B C}=\overrightarrow{O C}-\overrightarrow{O B} \\ &\overrightarrow{B C}=-3 \hat{\imath}+2 \hat{\jmath}-2 \hat{k} \\ &\overrightarrow{C A}=\overrightarrow{O A}-\overrightarrow{O C} \\ &\overrightarrow{C A}=0 \hat{\imath}-2 \hat{\jmath}-2 \hat{k} \end{aligned}

Now,

\begin{aligned} &\overrightarrow{B C} \cdot \overrightarrow{C A}=0-4+4 \\ &\overrightarrow{B C} \cdot \overrightarrow{C A}=0 \end{aligned}

So, \overrightarrow{BC} is perpendicular to .\overrightarrow{CA}

So, \Delta ABCis right angled at C.

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