Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Let x = i +3 j -2 k , y =2 i +4 j + k and a vector z satisfying x z = x y and z x =0 . Then [| z |] is greater than, (where [.] denotes greatest integer function)

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

x z = x y x ( z - y )=0 z - y = x z = y + x =2 i +4 j + k + ( i +3 j -2 k ) z =(2+ ) i + j (4+3 )+ k (1-2 ) z x =0 2+ +3(4+3 )-2(1-2 )=0 aligned & 2+ +12+9 -2+4 =0 & 14 =-12 aligned =- 6 7 so z = 8 7 i + 10 7 j + 19 7 k | z |= 1 7 8^2+10^2+19^2 [| z |]=3

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 Most Important Selected Qs for JEE Advanced PYQs