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  • Explain Solution R.D.Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 42 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 42 Maths Textbook Solution.

Answers (1)

Answer: Proved

Hint: You must know the rules of solving vectors.

Given: If \vec{a},\vec{b},\vec{c} are three non-coplanar vectors, such that \vec{a}.\vec{a}=\vec{d}.\vec{b}=\vec{d}.\vec{c}=0 then show that \vec{d} is the null vector.

Solution:

Given that \vec{a}\cdot \vec{a}=0

So, either \vec{a}=0or \vec{d}\perp\vec{a}

Similarly, \vec{d}\cdot \vec{b}=0

So, \vec{d}=0 or \vec{d}\perp\vec{b}

Also, \vec{d}\cdot \vec{c}=0

So, \vec{d}=0 or \vec{d}\perp \vec{c}

But \vec{d} cannot be perpendicular to \vec{a},\vec{b},\vec{c} as\vec{a},\vec{b},\vec{c} are non-coplanar

So, \vec{d}=0,\vec{d} is null vector.

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