Home
Class 12
MATHS
Let O be the origin and vec(OX) , vec(O...

Let O be the origin and` vec(OX) , vec(OY) , vec(OZ)` be three unit vector in the directions of the sides `vec(QR) , vec(RP),vec(PQ)` respectively , of a triangle PQR.
`|vec(OX)xxvec(OY)|=`

A

sin ( P +Q)

B

sin 2R

C

sin (P +R)

D

sin (Q +R)

Text Solution

Verified by Experts

The correct Answer is:
A
` | vec(OX) xx vec(OY)| `
` |vec(OX) ||vec(OY) | sin (pi -R) `
` sin R = sin ( pi - (P +Q)) = sin ( P +Q) " " [ P +Q +R = pi]`
Promotional Banner

Topper's Solved these Questions

  • SCALER AND VECTOR PRODUCTS OF TWO VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|12 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

  • SOLUTIONS OF TRIANGLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|20 Videos

Similar Questions

Explore conceptually related problems

Let O be the origin, and vector OX,OY,OZ be three unit vectors in the directions of the sides vectors QR,RP, PQ respectively, of a triangle PQR. Vector |vec(OX)=vec(OY)|= (A) sin2R (B) sin(P+R) (C) sin(P+Q) (D) sin(Q+R)

If vec(a) and vec(b) are the unit vectors and theta is the angle between them, then vec(a) + vec(b) is a unit vector if

The unit vector bisecting vec(OY) and vec(OZ) is

Let G be the centroid of Delta ABC , If vec(AB) = vec a , vec(AC) = vec b, then the vec(AG), in terms of vec a and vec b, is

Let vec a , vec b , vec c be the three unit vectors such that vec a+5 vec b+3 vec c= vec0 , then vec a. ( vec bxx vec c) is equal to

If vec(a) , vec( b) and vec( c ) are unit vectors such that vec(a) + vec(b) + vec( c) = 0 , then the values of vec(a). vec(b)+ vec(b) . vec( c )+ vec( c) .vec(a) is

vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c=0. then find the value of vec a. vec b+ vec b.vec c+ vec c. vec a

If vec(a) and vec(b) are unit vectors, then the angle between vec(a) and vec(b) for sqrt( 3) vec( a) - vec(b) to be a unit vector is

If OAB is a tetrahedron with edges and hatp, hatq, hatr are unit vectors along bisectors of vec(OA), vec(OB):vec(OB), vec(OC):vec(OC), vec(OA) respectively and hata=(vec(OA))/(|vec(OA)|), vecb=(vec(OB))/(|vec(OB)|), vec c= (vec(OC))/(|vec(OC)|) , then :

Let vec(p),vec(q),vec(r) be three unit vectors such that vec(p)xxvec(q)=vec(r) . If vec(a) is any vector such that [vec(a)vec(q)vec(r )]=1,[vec(a)vec(r)vec(p )]=2 , and [vec(a)vec(p)vec(q )]=3 , then vec(a)=