Vector Algebra — practice questions
33 curated practice questions from Vector Algebra (Mathematics JEE Main, NTA Exams) — 13 easy, 14 medium, 6 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.
- Given two vectors i - j and i +2 j . The unit vector coplanar with the two vectors and perpendicular to first is :
- Given three vectors a =6 i -3 j , ~b =2 i -6 j and c =-2 i +21 j such that r = a + b + c . Then the resolution of the…
- If the vectors i = i - j +2 k , b =2 i - j +2 k _ i and c = i + j + k _ i are mutually orthogonal, then ( , ) equals :
- Two vectors a = i + j 3 b = i 3 + j are
- a =3 i -5 j and b =6 i +3 j are two vectors and c is a vector such that c =[ a b ] . Then | r |:| b |:| c | is equal to
- If A=(2,3,-1) and B= (1_ 1 ,-1_ 1 , 2 ) . A point C on the y^ - axis, such that AB ⊥ BC, has the co-ordinates
- For non-zero vectors a , b , c ,|( a b ) c |=| a | b || c holds, if and only if
- The unit vector perpendicular to the vectors i - j + k and 2 i +3 j - k is:
- The vector i +x j +3 k is rotated through an angle θ and doubled in magnitude, then it becomes 4 i +(4 x-2) j +2 k …
- Given below are two statements. STATEMENT - 1: If three points P, Q and R have position vectors a , ~b and c…
- If a , b , c are unit vectors such that a ~b =0= a c and the angle between b and c is 3 . Then the value of | a b - a c…
- If a and b are two unit vectors such that a +2 b and 5 a -4 b are perpendicular to each other then the angle between a…
- If A, B, C, D are the points (2,3,-1) , (3,5,-3) , (1,2,3) , (3,5,7) respectively, then the angle between AB and CD is :
- Consider points A, B, C and D with position vectors 7 i -4 j +7 k , i -6 j +10 k , - i -3 j +4 k and i - j + k…
- Let r =( a b ) x+( b c ) y+2[ c a ] where a , b , c are three non-coplanar vectors. If r is perpendicular to a + b + c…
- Let a be real number and x = i +2 j , =2 i +a j +10 k , y =12 i +20 j +a k be three vectors, then x , and y are :
- If a and b are unit vectors, then the greatest value of | a + b |+| a - b | is
- Let I =3 i +2 j +2 k and b = i +2 j -2 k be two vectors. If a vector perpendicular to both the vectors a + b and a - b…
- The magnitude of the projection of the vector 2 i +3 j + k on the vector perpendicular to the plane containing the…
- The value of a, for which the points A, B, C with position vectors , and respectively are the vertices of a…
- Let a =a i +b j +c k , =b i +c j +a k and y =c i +a j +b k be three coplanar vectors with a ≠ b ≠ c and v = i + j + k …
- Given below are two statements. STATEMENT - 1: a b =(( i a ) b ) i +(( j a ) b ) j +(( k a ) b ) k STATEMENT - 2: c =(…
- Let a and b be two equal vectors inclined at an angle θ, then 2 is equal to :
- The (x, y, z) coordinates of two points A and B are given respectively as (0, 3, — 1) and ( — 2, 6, 4). The…
- Let a = i +2 j +4 k , b = i + j +4 k and c =2 i +4 j + (k^ 2 -1 ) k be coplanar vectors. Then the non-zero vector a c…
- If a =( -2) a + b and =(4 -2) a +3 b be two given vectors where vectors B and b are non-collinear. The value of for…
- Let i =2 i + j -2 k and b = i + j . if c is a vector such that a c =| c |,| c - a |=2 2 and the angle between ( a b )…
- If C is the midpoint of AB and P is any point outside AB, then :
- Let a and b be two equal vectors inclined at an angle θ, then 2.5 in 9 2 is equal to :
- Let A , E and C be unit vectors. Suppose A B = A C =0 and the angle between E and 屯 is 4 . Then :
- Find the projection of the line joining two points (2, -1, 4) and (3, 1, 2) on another line whose direction cosines are…
- If _ i=1 ^ n a _ i =0 , where | a _ i |=1 v i Z , then the value of _ 1 i<j n _ i n a _ i a _ j is :
- Let a =3 i +2 j +x k and b = i - j + k , for some real x. Then | a b |=r is possible if