Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202529 Jan 2025Evening ShiftMathematicsVector AlgebraActual

Let a be a unit vector perpendicular to the vectors b = i -2 j +3 k and c =2 i +3 j - k , and makes an angle of ⁻¹ (- 1 3 ) with the vector i + j + k . If a makes an angle of 3 with the vector i + j + k , then the value of is :

Options

  1. A6
  2. B- 6
  3. C- 3
  4. D3

Correct answer

B. - 6

Step-by-step solution

aligned & | array ccc i & j & k 1 & -2 & 3 2 & 3 & -1 array |= i (-7)+7 j +7 k & a = (-7 i +7 j +7 k ) 7^2+7^2+7^2 = ( - i + j + k 3 ) aligned aligned & Now, = (-1+1+1) 3 3 = 1 3 & ⁻¹ ( -1 3 ) a = -(- i + j + k ) 3 & a = i - j - k 3 aligned aligned & 3 = 1- -1 3 ^2+2 & 1 2 = - 3 ^2+2 < 0 & 3 ( ^2+2 )=4 ^2 & 6= ^2 & = 6 aligned Clearly, =- 6

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