Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

A unit vector in x y- plane which makes an angle of 45^ with the vector i + j and an angle of 60^ with the vector 3 i - 4 j is

Options

Ai
Bi + j 2
Ci - j 2
Dnone of these

Correct answer

D. none of these

Step-by-step solution

Let r =a i +b j a^2+b^2=1 ....(1) Also, 45^ = r ( i + j ) | r || i + j | a+b=1 ....(2) 60^ = r (3 i -4 j ) | r ||3 i -4 j | 3 a-4 b= 5 2 ....(3) There exists no real values of a and b satisfying (1), (2) and (3) Hence no such unit vector exists

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 Most Important Selected Qs for JEE Advanced PYQs