KCET2012MathematicsVector Algebra

If i + j - k and 2 i -3 j + k are adjacent sides of a parallelogram, then the lengths of its diagonals are

Options

A3 , 14
B13 , 14
C21 , 3
D21 , 13

Correct answer

D. 21 , 13

Step-by-step solution

array ll Let & A B = i + j - k and & B C =2 i -3 j + k array The diagonal A C = A B + B C aligned &=( i + j - k )+(2 i -3 j + k ) &=3 i -2 j aligned The length of diagonal A C = (3)²+(-2)² = 9+4 = 13 The diagonal D B = A B - A D aligned &=( i + j - k )-(2 i -3 j + k ) &=- i +4 j -2 k aligned The length of diagonal DB = 1+16+4 = 21

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 KCET PYQs