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  • Explain Solution R.D.Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.3 Question 6 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 22 Algebra of Vectors  Exercise 22.3 Question 6 Maths Textbook Solution.

Answers (1)

Answer:\frac{-5 p+6 \vec{r}}{11} o r \frac{2 \vec{q}+9 \vec{s}}{11}

Hint: Use vector algebra.

Given: 5 \vec{p}-2 \vec{q}+6 \vec{r}-9 \vec{s}=0

Solution: 5 \vec{p}-6 \vec{r}=2 \vec{q}-9 \vec{s}

\frac{-5 p+6 \vec{r}}{11} =\frac{2 \vec{q}+9 \vec{s}}{11}....(1)                                       

                                                                                          

As we know that,  if the point C divides the line segment AB in the ratio m:n the  \overrightarrow{O C}=\frac{n \overrightarrow{O A}+m \overrightarrow{O B}}{m+n}

let AB the point which PR in the ratio 6:5 and B be the point which divides QS in the ratio 9:2 .hence the P.V of AB are \frac{6 \vec{p}+6 \vec{r}}{11}, \frac{2 \vec{q}+9 \vec{s}}{11}

From (1)

The P.V of AB is same.

=  point A and B intersect at the same point

=  PQ and QS intersect at A

 of two line segment intersect then it must be Co-planner.

P,Q,R,S are co-planner.

 

 

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