JEE Advanced2006MathematicsVector AlgebraActual

Match the following

Options

A(i) (a), (ii) (b), (iii) (d), (iv) (c)
B(i) (c), (ii) (a), (iii) (b), (iv) (d)
C(i) (a), (ii) (d), (iii) (b), (iv) (c)
D(i) (b), (ii) (a), (iii) (c), (iv) (d)

Correct answer

D. (i) (b), (ii) (a), (iii) (c), (iv) (d)

Step-by-step solution

(i) Solved the two equations, say, i.e. x+y=|a| and a x-y=1 , we get x= |a|+1 a+1 >0 and y= |a|-1 a+1 >0 when a+1>0 ; we get a>1 a₀=1 (ii) We have, a = i + j + k a k = Now, k ( k a )=( k a )-( k k ) a = k -( i + j + k ) i + j =0 = =0 Also, + + =2 =2 (iv) A B C+ A B A B+ A B= (A-B) array lc & (A-B) 1 (A-B)=1 & C=1 array

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 , 2026 Let 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: 2026 Let 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 : 2026 If 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 _______. 2026 Let 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 : 2026 Let 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: 2026 Let 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: 2026 Let 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 Advanced PYQs