For any four points P- Q- R- S- - -PQ - RS - QR - PS - RP - QS- is equal to 4 times the area of the triangle-

The correct option is B QRS P⃗Q⃗×R⃗S⃗ Q⃗R⃗×P⃗S⃗+R⃗P⃗×Q⃗S⃗ =(P⃗S⃗+S⃗Q⃗)×R⃗S⃗ Q⃗R⃗×P⃗S⃗+(R⃗S⃗+S⃗P⃗)×Q⃗S⃗ =P⃗S⃗× (R⃗S⃗+S⃗Q⃗+Q⃗R⃗) S⃗Q⃗×S⃗R⃗ S⃗Q⃗×S⃗R⃗ ...

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Byju's Answer

Standard IX

Mathematics

Scale Factor of Length

For any four ...

Question

For any four points P, Q, R, S,
$\to\to\to\to\to\to$
$| P Q \times R S - Q R \times P S + R P \times Q S |$ is equal to 4 times the area of the triangle.

PQR

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QRS

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PRS

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PQS

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Solution

The correct option is B QRS
$\to P Q \times \to R S - \to Q R \times \to P S + \to R P \times \to Q S$
$= (\to P S + \to S Q) \times \to R S - \to Q R \times \to P S + (\to R S + \to S P) \times \to Q S$
$= \to P S \times (\to R S + \to S Q + \to Q R) - \to S Q \times \to S R - \to S Q \times \to S R$
$= \to P S \times \to O - 2 \to S Q \times \to S R$
$= 4 \times$ area of $△ Q R S$
correct answer in option $(B) Q R S$

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Q. Question 12
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Q. For any four points

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For any four points P, Q, R, S,→→→→→→|PQ×RS−QR×PS+RP×QS| is equal to 4 times the area of the triangle.

The correct option is B QRS→PQ×→RS−→QR×→PS+→RP×→QS=(→PS+→SQ)×→RS−→QR×→PS+(→RS+→SP)×→QS=→PS×(→RS+→SQ+→QR)−→SQ×→SR−→SQ×→SR=→PS×→O−2→SQ×→SR=4× area of △QRScorrect answer in option (B) QRS

For any four points P, Q, R, S,
$\to\to\to\to\to\to$
$| P Q \times R S - Q R \times P S + R P \times Q S |$ is equal to 4 times the area of the triangle.