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

The correct option is A 9p^2=4q^2 O #160;is the origin. #160; R #160;divides #160; PQ #160;internally in the ratio #160; 2 ...

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Byju's Answer

Standard XII

Mathematics

Particular Solution of a Differential Equation

Let p⃗ and ...

Question

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

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

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

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9 p = 4 q

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4 p = 9 q

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Solution

The correct option is A $9 p^{2} = 4 q^{2}$
$O$ is the origin. $R$ divides $P Q$ internally in the ratio $2 : 3$ ,
$\Rightarrow \to r = \frac{3 \to p + 2 \to q}{3 + 2}$
Also, $\to s = \frac{3 \to p - 2 \to q}{3 - 2}$
Because its given that $O R$ is perpendicular to $O S$ , their dot product equals $0$ .
$∴$ $\frac{1}{5} (3 \to p + 2 \to q) . (3 \to p - 2 \to q) = 0$
$\Rightarrow$ $9 p^{2} = 4 q^{2}$

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Similar questions

Q. 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 .

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

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

Q. lf

\to P \times \to Q = \to R; \to Q \times \to R = \to P

and

\to R \times \to P = \to Q

are 3 non-zero vectors, then,
a)

\to P, \to Q

and

\to R

are coplanar
b) Angle between

\to P

and

\to Q

may be less than

90^{0}

\to P + \to Q + \to R

cannot be equal to zero
d)

\to P, \to Q

and

\to R

are mutually perpendicular
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P \neq Q \neq R \neq 0

)

Q. Three vectors

\to P

\to Q

\to R

are such that the

| \to P |

= | \to Q |

| \to R |

= \sqrt{2}

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and

\to P + \to Q

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

The correct option is A 9p2=4q2O is the origin. R divides PQ internally in the ratio 2:3, ⇒→r=3→p+2→q3+2Also, →s=3→p−2→q3−2Because its given that OR is perpendicular to OS, their dot product equals 0.∴ 15(3→p+2→q).(3→p−2→q)=0⇒ 9p2=4q2

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