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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 19 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot  Products  Exercise 23.1 Question 19 Maths Textbook Solution.

Answers (1)

Answer: proved

Hint: you must know the rules of solving vectors

Given: \vec{b}=\hat{i}-3\hat{j}+5\hat{k},

\vec{c}=2\hat{i}+\hat{j}-4\hat{k}, form a right angle

Solution: Let ABC be the given triangle

\begin{aligned} &\overrightarrow{A C}=\vec{b}=\hat{\imath}-3 \hat{\jmath}+5 \hat{k} \\ &\overrightarrow{C B}=\vec{a}=3 \hat{\imath}-2 \hat{\jmath}+\hat{k} \\ &\overrightarrow{A B}=\vec{c}=2 \hat{\imath}+\hat{\jmath}-4 \hat{k} \\ &\vec{a} \cdot \vec{b}=3+6+5=14 \\ &\vec{b} \cdot \vec{c}=2-3-20=-21 \\ &\vec{a} \cdot \vec{c}=6-2-4=0\\&\operatorname{So} \overrightarrow{A B} \text { is } \perp \text { to } \overrightarrow{CB} \end{aligned}                                                \mid \therefore \Delta ABC \text{is a right angle triangle} \mid

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