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Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors Exercise Very Short Answer Question 5 Maths textbook Solution.

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Answer: $X=0,Y=0$

Hint: You must know the rules of vector functions.

Given: If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors, such that $x\vec{a}+y\vec{b}=\vec{0}$ , then write the values of $x$ and $y$

Solution: We have, $\vec{a}$ and $\vec{b}$ are non-collinear vectors and $x\vec{a}+y\vec{b}=\vec{0}$

$\Rightarrow \frac{a}{b}=-\frac{y}{x}$

Given that $\vec{a}$ and $\vec{b}$ are non collinear , so $\vec{a}$ and $\vec{b}$ should not be parallel ,

Therefore, $\frac{y}{x}=0$

$\Rightarrow y=0$

Similarly , the given equation can also be written as $\frac{b}{a}=-\frac{x}{y}$

Given that $\vec{a}$ and $\vec{b}$ are non collinear , so $\vec{a}$ and $\vec{b}$ should not be parallel ,

Therefore, $\frac{x}{y}=0$

$\Rightarrow x=0$

Hence we get , $x=0$ and $y=0$

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