Let $O$ be the origin, and $- - \to O X, - - \to O Y, - - \to O Z$ be three unit vectors in the directions of the sides $- - \to Q R, - - \to R P, - - \to P Q,$ respectively, of a triangle $P Q R .$

$| - - \to O X \times - - \to O Y | =$

sin (P + Q)

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sin 2 R

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sin (P + R)

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sin (Q + R)

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Solution

The correct option is A $sin (P + Q)$
$| - - \to O X \times - - \to O Y | = | - - \to O X | | - - \to O Y | sin (R) = sin (π - R) = sin (P + Q)$

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Similar questions

Q. Let

O

be the origin, and

- - \to O X, - - \to O Y, - - \to O Z

be three unit vectors in the directions of the sides

- - \to Q R, - - \to R P, - - \to P Q,

respectively, of a triangle

P Q R .

| - - \to O X \times - - \to O Y | =

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, PQ respectively, of a triangle PQR.
$| O X \times O Y | =$

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, PQ respectively, of a triangle PQR.
If the triangle PQR varies, then the minimum value of $cos (P + Q) + cos (Q + R) + cos (R + P)$ is

Q. Let

O

be the origin, and

- - \to O X, - - \to O Y, - - \to O Z

be three unit vectors in the directions of the sides

- - \to Q R, - - \to R P, - - \to P Q,

respectively, of a triangle

P Q R .

If the triangle

P Q R

varies, then the minimum value of

cos (P + Q) + cos (Q + R) + cos (R + P)

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Let O be the origin, and −−→OX,−−→OY,−−→OZ be three unit vectors in the directions of the sides −−→QR,−−→RP,−−→PQ, respectively, of a triangle PQR. |−−→OX×−−→OY|=

The correct option is A sin(P+Q)|−−→OX×−−→OY|=|−−→OX||−−→OY|sin(R)=sin(π−R)=sin(P+Q)

Let $O$ be the origin, and $- - \to O X, - - \to O Y, - - \to O Z$ be three unit vectors in the directions of the sides $- - \to Q R, - - \to R P, - - \to P Q,$ respectively, of a triangle $P Q R .$

$| - - \to O X \times - - \to O Y | =$

The correct option is A $sin (P + Q)$
$| - - \to O X \times - - \to O Y | = | - - \to O X | | - - \to O Y | sin (R) = sin (π - R) = sin (P + Q)$