Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20236 Apr 2023Evening ShiftMathematicsVector AlgebraActual

The sum of all values of α , for which the points whose position vectors are i ^ - 2 j ^ + 3 k ^ , 2 i ^ - 3 j ^ + 4 k ^ , α + 1 i ^ + 2 k ^ and 9 i ^ + α - 8 j ^ + 6 k ^ are coplanar, is equal to

Options

  1. A- 2
  2. B2
  3. C6
  4. D4

Correct answer

B. 2

Step-by-step solution

Let the given vectors be A → = i ^ - 2 j ^ + 3 k ^ ,   B → = 2 i ^ - 3 j ^ + 4 k ^ ,   C → = α + 1 i ^ + 2 k ^   and   D → = 9 i ^ + α - 8 j ^ + 6 k ^ We know that if the vectors are coplanar then A B → A C → A D → = 0 ⇒ A B → = 2 i ^ - 3 j ^ + 4 k ^ - i ^ - 2 j ^ + 3 k ^ = i ^ - j ^ + k ^ ⇒ A C → = α + 1 i ^ + 2 k ^ - i ^ - 2 j ^ + 3 k ^ = α i ^ + 2 j ^ - k ^ ⇒ A D → = 9 i ^ + α - 8 j ^ + 6 k

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