Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainMathematicsVector Algebra

Let u = 2 i + j + k and v = i - 2 j + 2 k be two vectors. If the magnitude of the projection of u on v is 2 and the direction of the projection vector is opposite to the direction of v , then the value of is

Options

  1. A-1
  2. B5
  3. C1
  4. D-5

Correct answer

B. 5

Step-by-step solution

Given vectors are u = 2 i + j + k and v = i - 2 j + 2 k . The magnitude of v is: | v | = (1)^2 + (-2)^2 + (2)^2 = 1 + 4 + 4 = 3 The dot product of u and v is: u v = (2)(1) + ( )(-2) + (1)(2) = 4 - 2 The scalar projection of u on v is given by u v | v | . Since the magnitude of the projection is 2 and its direction is opposite to v , the scalar projection must be strictly negative. Thus, the scalar projection is -2 . Equating the two expressions for the scalar projection: 4 - 2 3 = -2 4 - 2 = -6 -2 = -10 = 5 Answer:

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 Main PYQs