MHT CET202312 May 2023Evening ShiftMathematicsVector AlgebraActual

If a , b , c are three non-zero vectors, no two of them are collinear, a +2 b is collinear with c , b +3 c is collinear with a , then a +2 b is

Options

A6 c _c
B-6 c
Cc
D2 c

Correct answer

B. -6 c

Step-by-step solution

array ll & a +2 b is collinear with c & a +2 b = n c & Similarly b +3 c = ma & m and n are non-zero scalars. & (i) a +2 b +6 c =( n +6) c & (ii) a +2 b +6 c =(2 ~m +1) a n +6=0 and 2 ~m +1=0 n =-6 and m = -1 2 & (i) a +2 ~b =-6 c array

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 2025 If 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 2025 The 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 2025 Let 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 2025 If 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 2025 Let 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 2025 If 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 2025 If 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 MHT CET PYQs