Let p and q be the position vectors of points P and Q respectively with respect to origin O and -p-p-q-q- If R-S divide PQ internally and externally in the ratio 2-3 respectively- If OR and OS are perpendicular- then

Given : R divides PQ internally in ratio 2:3 ⇒OR=3p+2q3+2 Also, nbsp;S divides PQ externally in ratio 2:3 ⇒ nbsp; nbsp;OS=3p 2q3 2 As, OR and OS are perp ...

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Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

Let p and q b...

Question

Let $\to p$ and $\to q$ be the position vectors of points $P$ and $Q$ respectively with respect to origin $(O)$ and $| \to p | = p, | \to q | = q .$ If $R, S$ divide $P Q$ internally and externally in the ratio $2 : 3$ respectively. If $- - \to O R$ and $- - \to O S$ are perpendicular, then

4 p^{2} = 9 q^{2}

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9 p^{2} = 4 q^{2}

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3 p^{2} = 2 q^{2}

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p^{2} = q^{2}

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Solution

The correct option is B $9 p^{2} = 4 q^{2}$
Given : $R$ divides $P Q$ internally in ratio $2 : 3$
$\Rightarrow - - \to O R = \frac{3 \to p + 2 \to q}{3 + 2}$
Also, $S$ divides $P Q$ externally in ratio $2 : 3$
$\Rightarrow - - \to O S = \frac{3 \to p - 2 \to q}{3 - 2}$

As, $- - \to O R$ and $- - \to O S$ are perpendicular
$∴ - - \to O R \cdot - - \to O S = 0$
$\Rightarrow (\frac{3 \to p + 2 \to q}{3 + 2}) \cdot (\frac{3 \to p - 2 \to q}{3 - 2}) = 0$
$∴ 9 p^{2} = 4 q^{2}$
$(∵ | \to p | = p, | \to q | = q)$

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Similar questions

Q. Let

\to p

and

\to q

be the position vectors of

P

and

Q

respectively with respect to

O

and

| \to p | = p, | \to q | = q .

The points

R

and

S

divides

P Q

internally and externally in the ratio

3 : 2

respectively. If

- - \to O R

and

- - \to O S

are perpendicular, then

P, Q

have position vectors

\to a

and

\to b

relative to the origin

O

and

X, Y

divide

- - \to O Q

internally and externally respectively in the ratio

2 : 1

. Vector

- - \to X Y =

Q. Let

\to p

and

\to q

be the position vectors of

P

and

Q

respectively with respect to

O

and

| \to p | = p, | \to q | = q

R, S

divide

P, Q

Internally and externally in the ratio

2 : 3

respectively. If

O R

and

O S

are perpendicular, then

Q. The position vectors of the points

A, B

and

C

are respectively

\to a, \to b

and

\to c .

P

divides

- - \to A B

in the ratio

3 : 4

and

Q

divides

- - \to B C

in the ratio

2 : 1

both externally, then

- - \to P Q

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and

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are two points with position vectors

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and

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respectively. Write the position vector of a point R which divides the line segment

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Addition and Subtraction in Unit Vector Notation

Standard XII Physics

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Let →p and →q be the position vectors of points P and Q respectively with respect to origin (O) and |→p|=p,|→q|=q. If R,S divide PQ internally and externally in the ratio 2:3 respectively. If −−→OR and −−→OS are perpendicular, then

Let $\to p$ and $\to q$ be the position vectors of points $P$ and $Q$ respectively with respect to origin $(O)$ and $| \to p | = p, | \to q | = q .$ If $R, S$ divide $P Q$ internally and externally in the ratio $2 : 3$ respectively. If $- - \to O R$ and $- - \to O S$ are perpendicular, then