Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

Let a =2 i + j -2 k , b = i + j and c be a vector such that | c - a |=3 . If p = a b , then the angle between p and c is 6 and | p c |=3 . Thus a . c is equal to-

Options

  1. A1 8
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

Given a =2 i + j -2 k , b = i + j ,| c - a |=3 p = a b ,| p c |=3 and angle between p and c is 6 Here, p = a b = | array ccc i & j & k 2 & 1 & -2 1 & 1 & 0 array |=2 i -2 j + k | p |=3 also | a |=3 and | b |= 2 aligned & Now | p c |=3 | p || c | 6 =3 & 3| c | 1 2 =3 & | c |=2 & and | c - a |=3 | c - a |^2=9 & | c |^2+| a |^2-2 c a =9 & 4+9-2 a c =9 aligned a c =2

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 99 Percentile Qs Bank for JEE Main PYQs