Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201822 Apr 2018Morning ShiftMathematicsVector AlgebraActual

Let a , b and c be three non-coplanar vectors. The vector equation of a line which passes through the point of intersection of two lines, one joining the points a +2 b -5 c , - a -2 b -3 c and the other joining the points -4 c , 6 a -4 b +4 c is

Options

  1. Ar=2 a-4 b+3 c+ (a-6 b+4 c)
  2. Br=3 a+6 b-c+ (a+2 b+c)
  3. Cr =2 a +3 ~b - c + ( a + b - c )
  4. Dr=-2 b+3 c+ (a-4 b+3 c)

Correct answer

B. r=3 a+6 b-c+ (a+2 b+c)

Step-by-step solution

Equation of line joining the points, a +2 b -5 c ,- a -2 b -3 c is r =( a +2 b -5 c )+ ₁,(2 a +4 b -2 c ) Similarly, equation of the line joining the points -4 c, 6 a-4 b+4 c is r =-4 c + ₂(6 a -4 b +8 c ) Now, for point of intersection of lines (i) and (ii) aligned (2 ₁+1 ) a + & (4 ₁+2 ) b + (-2 _ , -5 ) c = & (6 ₂ ) a + (-4 ₂ ) b + (8 ₂+4 ) c aligned On comparing aligned 2 ₁+1 & =6 ₂ 4 ₁+2 & =-4 ₂ -2 ₁-5 & =8 ₂+4 aligned and From Eqs. (iii), (iv) and (v) ₁=- 1 2 and ₂=0 So, intersection points is -4 c and for =-

Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

P is the circumcentre of A B C . If the position vectors of A, B, C and P are a , b , c , a + b + c 4 respectively, then the position vector of the orthocentre of this triangle is 2025If the position vectors of A, B, C, D are i +2 j +2 k , 2 i - j , i + j +3 k and 4 j +5 k respectively, then the quadrilateral ABCD is a 2025The set of all real values of c so that the angle between the vectors a = cx i -6 j +3 k and b =x i +2 j +2 cx k is an obtuse angle for all real x is 2025Let a =2 i + j +3 k , b =3 i +3 j + k and c = i -2 j +3 k be three vectors. If r is a vector such that r a = r b and r c =18 , then the magnitude of the orthogonal projection of 4 2025If u , v , w are non coplanar vectors and p, q are real numbers, then the equality [ array lll 3 u & p v & p w array ]- [ array lll p v & w & q u array ]- [ array lll 2 w & q v & q 2025Let i -2 j + k , i + j -2 k , 2 i - j - k and i + j + k be the position vectors of four points A , B , C and D respectively. If a point P divides AB in the ratio 2: 1 internally an 2025If a = i + j , b =2 j - k are two vectors such that r a = b a , r b = a b , then the unit vector in the direction of r is 2025If a , b , c are three unit vectors such that a ( b c )= 3 2 b + c 2 and , are the angles between a , c and a , b respectively, then + = 2025 Full Vector Algebra list All AP EAMCET PYQs