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  • Explain Solution R.D. Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 50 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 50 Maths Textbook Solution.

Answers (1)

Answer:\frac{\pi }{3}

Hints: You must know the rules of solving vectors.

Given: Let \vec{a} and \vec{b} be unit vector. If the vectors \vec{c}=\vec{a}+2\vec{b},\vec{d}=5\vec{a}-4\vec{b} ,  are perpendicular to each other. Find the angle between vector \vec{a} and \vec{b}

Solution: a and b are unit vectors, ie, \mid a\mid =\mid b\mid =1

                                                          \vec{c}=\vec{a}+2\vec{b}\: \: and\: \: \vec{d}=5\vec{a}-4\vec{b}

c and d are perpendicular to each other,

c\cdot d=0

Angle between a and b

\begin{aligned} &c \cdot d=0 \\ &(a+2 b)(5 a-4 b)=0 \\ &5 a \cdot a-4 a \cdot b+10 b \cdot a-8 b \cdot b=0 \\ &6(a \cdot b)=3 \\ &a \cdot b=\frac{1}{2} \quad \therefore\left[\text { because } \cos ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}\right] \end{aligned}

So, angle between a and b is \frac{\pi }{3}

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