Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2017MathematicsVector AlgebraActual

Paragraph: Let O be the origin, and O X , O Y , O Z be three unit vectors in the directions of the sides Q R , R P , P Q , respectively, of a triangle P Q R . Question: | O X O Y |=

Options

  1. Asin P + Q
  2. Bsin   2 R
  3. Csin P + R
  4. Dsin Q + R

Correct answer

A. sin P + Q

Step-by-step solution

O X → ,   O Y → ,   O Z → are unit vectors in the directions of sides O R → ,   R P → and P Q → respectively, ∴    O X → = Q R → Q R → ,    O Y → = R P → R P → ,   O Z → = P Q → P Q →   ∴    O X → × O Y → = O R → × R P → Q R →   R P → = Q R →   R P → sin P + Q Q R →   R

Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

Let a , b be two vectors, and let P, Q and R be the points with position vectors a , b and a + b , respectively, with respect to the origin O . If | a + b | = 21 , | a - b | = 3 , 2026Let a = 4 i - j + 3 k , b = 10 i + 2 j - k and a vector c be such that 2( a b ) + 3( b c ) = 0 . If a c = 15 , then c ( i + j -3 k ) is equal to: 2026Let a = 2 i + 3 j + 3 k and b = 6 i + 3 j + 3 k . Then the square of the area of the triangle with adjacent sides determined by the vectors (2 a + 3 b ) and ( a - b ) is : 2026If a = i + j + k , b = j - k and c be three vectors such that a c = b and a c = 3 , then c ( a - 2 b ) is equal to _______. 2026Let O be the origin, OP = a and OQ = b . If R is the point on OP such that OP = 5 OR , and M is the point such that OQ = 5 RM , then PM is equal to : 2026Let a = 7 i + j - k and b = j + 2 k . If r is a vector such that r a + a b = 0 and r a = 0 , then |3 r |^2 is equal to: 2026Let u and v be unit vectors inclined at an acute angle such that | u v |= 3 2 . If A = u + v +( u v ) , then is equal to: 2026Let a_k = ( _k) i + j and b_k = i - ( _k) j , where _k = 2^ k-1 2^n + 1 , for some n N , n > 5 . Then the value of _ k=1 ^ n | a_k |^2 _ k=1 ^ n | b_k |^2 is _____. 2026 Full Vector Algebra list All JEE Advanced PYQs