Vector Algebra — practice questions

29 curated practice questions from Vector Algebra (Mathematics JEE Advanced, NTA Exams) — 29 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.

• Let a = i - j , b = j - k , c = k - i . If is a unit vector such that a d =0=[ b c d ] , then equals
• The volume of the parallelopiped whose sides are given by O A =2 i -3 j , O B = i + j - k , O C =3 i - k is
• Let p and q be the position vectors of P and Q respectively, with respect to O and | p |=p,| q |=q . The points R and S…
• The unit vector which is orthogonal to the vector 5 i +2 j +6 k and is coplanar with the vectors 2 i + j + k and i - j…
• Let a and b be positive real numbers. Suppose are adjacent sides of a parallelogram PQRS . Let u ext and v be the…
• The scalar A ( B + C ) ( A + B + C ) equals
• If a , b , c and are unit vectors such that ( a b ) ( c d )=1 and a c = 1 2 , then
• If a , b and c are unit coplanar vectors, then the scalar triple product [ array lll 2 a - b & 2 b - c & 2 c - a array…
• Let the vectors a , b , c ext and d be such that ( a imes b ) imes( c imes d )= 0 . Let P 1 and P 2 be planes…
• Let the position vectors of the points P , Q , R and S be a = i +2 j -5 k , b =3 i +6 j +3 k , c = 17 5 i + 16 5 j +7 k…
• If and are two unit vectors such that a +2 b and 5 a -4 b are perpendicular to each other then the angle between and is
• The points with position vectors 60 i +3 j , 40 i -8 j , a i -52 j are collinear if
• Let i, j ext and k be the unit vectors along the three positive coordinate axes. Let a =3 i + j - k b = i +b_ 2 j +b_ 3…
• Let a =2 i + j + k , b = i +2 j - k and a unit vector be coplanar. If is perpendicular to , then =
• Let p , q , r be three mutually perpendicular vectors of the same magnitude. If a vector satisfies the equation p…
• Let a , b , c be distinct non-negative numbers. If the vectors a i +a j +c k , i + k and c i +c j +b k lie in a plane…
• The vector(s) which is/are coplanar with vectors i + j +2 k and i +2 j + k , and perpendicular to the vector i + j + k…
• Let v =2 i + j - k , w = i +3 k and u is a unit vector then the maximum value of [ array lll u & v & w array ] is
• Let a =2 i + j -2 k and b = ilde i + j . If is a vector such that , | c - a |=2 2 and the angle between is 30°, than
• The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a , b , c such that a b…
• The number of distinct real values of λ, for which the vectors - ^ 2 i + j + k , i - ^ 2 j + k and are coplanar, is
• Let a = i - k , b =x i + j +(1-x) k and c =y i +x j +(1+x-y) k . Then [ array lll a & b & c array ] depends on
• Let a =a_ 1 i +a_ 2 j +a_ 3 k , +c_ 2 j +c_ 3 k be three non-zero vectors such that is a unit vector perpendicular to…
• Let be vector parallel to line of intersection of planes P 1 and P 2 . Plane P 1 is parallel to the vectors 2 j +3 k…
• Let P R =3 i + j -2 k and S Q = i -3 j -4 k determine diagonals of a parallelogram PQRS and P T = i +2 j +3 k be…
• The value of ‘ a ’ so that the volume of parallelopiped formed by i +a j + k , j +a k and a i + k becomes minimum is
• Two adjacent sides of a parallelogram ABCD are given by A B =2 i +10 j +11 k and A D =- i +2 j +2 k . The side AD is…
• If a = i + j + k , b =4 i +3 j +4 k and c = i + j + k are linearly dependent vectors and | c |= 3 , then
• If a , b and c are three non coplanar vectors, then ( a + b + c ) [( a + b ) ( a + c )] equals

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