NDA Vector Algebra questions with solutions
Vectors, scalar and vector products. 60 questions from our 2016–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
Also practise: Vector Algebra for JEE Main · Vector Algebra for JEE Advanced
NDA 2025
- For two non-zero vectors, the dot product equals the magnitude of the cross product. The angle between the vectors is then
- The vector with initial point (1,2,3) and terminal point (3,5,9) has magnitude
- The vector equation of the line passing through the point with position vector 2hat i+hat j and parallel to the vector 3hat j-hat k is
- If vec a·vec b=0 and vec a×vec b=vec 0, then
- The position vector of the midpoint of the segment joining A(2,3,1) and B(4,-1,3) is
- If vec a,vec b,vec c are three mutually perpendicular unit vectors, then |vec a+vec b+vec c| is equal to
- The scalar triple product of three coplanar vectors is zero. 2. For any vector vec a, vec a×vec a is the zero vector.
NDA 2024
- Three mutually perpendicular vectors vec a, vec b, vec c have magnitudes 1, 2 and 2 respectively. The magnitude of vec a+vec b+vec c is
- If vec a=hat i+λhat j+2hat k and vec b=3hat i-hat j+hat k have equal magnitudes, then λ equals
- The angle which the vector hat i+hat j+hat k makes with the x-axis is
- The area of the triangle with vertices at the origin, 2hat i+hat j and hat i+3hat j is
- The component (scalar projection) of 3hat i+4hat j along hat i+hat j is
- Let vec u and vec v be any two vectors in space. 1. |vec u·vec v|≤|vec u||vec v|. 2. |vec u+vec v|≥|vec u|+|vec v|.
NDA 2023
- If vec a and vec b are perpendicular vectors with |vec a|=3 and |vec b|=4, then |vec a+vec b| is
- The sides of a triangle, taken in order, are represented by vectors vec a,vec b,vec c of lengths 3, 5 and 7 units so that their sum is the zero…
- If vec a and vec b are non-zero vectors with |vec a+vec b|=|vec a-vec b|, then the angle between vec a and vec b is
- If A and B have position vectors vec a and vec b, the position vector of the point dividing AB externally in the ratio 3:1 is
- Hat i·(hat j×hat k)=1. 2. For any vector vec a, vec a×vec a=|vec a|^2.
NDA 2022
NDA 2021
- If vec a·vec b=|vec a×vec b| for two non-zero vectors, the angle between them is
- A vector perpendicular to both hat i+hat j and hat j+hat k is
- The moment about the origin of the force hat i+2hat j+3hat k acting at the point with position vector hat i+hat j is
- For any vectors vec a and vec b, vec a×vec b is parallel to vec a. 2. The scalar product vec a·vec b is a vector.
- If |vec a|=3, |vec b|=4, then |vec a×vec b|^2+(vec a·vec b)^2 is equal to
- The point dividing the join of P(2hat i+3hat j-hat k) and Q(6hat i-hat j+3hat k) internally in the ratio 1:3 has position vector
NDA 2020
- A vector of magnitude 14 in the direction of 2hat i+3hat j+6hat k is
- The area of the parallelogram having adjacent sides vec a=hat i+2hat j and vec b=3hat i-hat j is
- If the vectors 2hat i-3hat j+6hat k and μhat i+6hat j-12hat k are parallel, then μ is
- The volume of the parallelepiped whose coterminous edges are vec a=hat i+2hat j-hat k, vec b=3hat i+2hat k and vec c=-2hat i+hat j+hat k is
- The scalar projection of hat i+2hat k on 2hat i+3hat j+6hat k is
- Two statements about the magnitudes of vector sums and products are given below, for any vectors vec a and vec b. 1. |vec a+vec b|≤|vec a|+|vec b|.…
- If vec a,vec b,vec c are unit vectors such that vec a+vec b+vec c=vec 0, then vec a·vec b+vec b·vec c+vec c·vec a is equal to
NDA 2019
- The unit vectors vec a and vec b satisfy |vec a+vec b|=1. The angle between vec a and vec b is
- The points P and Q have position vectors hat i+2hat j and 3hat i-2hat j. The point R divides PQ externally in the ratio 3:1. The position vector of R…
- The vector hat i+hat j+√2 hat k makes an angle θ with the positive direction of the z-axis. Then θ equals
- A force vec F=hat i+2hat j+3hat k acts at the point (1,-1,2). Its moment about the origin is
- If [vec a vec b vec c]=vec a·(vec b×vec c)=4, then (vec a+vec b)·[(vec b+vec c)×(vec c+vec a)] equals
- If |vec a×vec b|=12 and vec a·vec b=5, then |vec a| |vec b| is equal to
- Three vectors are coplanar if and only if their scalar triple product is zero. 2. Interchanging any two of the three vectors in [vec a vec b vec c]…
NDA 2018
- If vec a=2hat i-hat k and vec b=hat i+3hat j+2hat k, then |vec a×vec b| equals
- If |vec a|=|vec b|=|vec a+vec b| for non-zero vectors, the angle between vec a and vec b is
- The vectors hat i+2hat j-hat k, 2hat i+hat j+λhat k and hat i-hat j+2hat k are coplanar if λ equals
- If |vec a|=2 and |vec b|=3, then |vec a×vec b|^2+(vec a·vec b)^2 equals
- If vec a×vec b=vec 0, then either vec a=vec 0 or vec b=vec 0. 2. If vec a·vec b=0, then vec a and vec b are perpendicular or at least one of them is…
- The triangle with vertices P(1,2,3), Q(4,2,3) and R(1,6,3) is
- A vector vec a satisfies vec a·hat i=vec a·(hat i+hat j)=vec a·(hat i+hat j+hat k)=1. Then vec a equals
NDA 2017
- If |vec a|=1, |vec b|=2 and the angle between them is 120^°, then |2vec a+vec b| equals
- The component of vec a=2hat i+3hat j-hat k along vec b=hat i-2hat j+2hat k is
- The sine of the angle between vec a=hat i+2hat j+2hat k and vec b=3hat j+4hat k is
- The vectors phat i+hat j+hat k and hat i+phat j+hat k make an angle of 60^° with each other. The non-zero value of p is
- Three concurrent edges of a tetrahedron are hat i+2hat j, hat j+2hat k and 2hat i+hat k. Its volume is
- The vectors hat i+2hat j+3hat k and 2hat i+4hat j+6hat k are collinear. 2. The vectors hat i+hat j, hat j+hat k and hat k+hat i are coplanar.
- Examine the following assertions about non-zero vectors vec p,vec q,vec r: 1. vec p·vec q=0 for every pair of mutually perpendicular vectors. 2. If…
- The angle between the vectors hat i+2hat j+2hat k and 2hat i-2hat j+hat k is
NDA 2016
- If vec a=hat i+hat j and vec b=hat j+hat k, then |vec a×vec b| is equal to
- The area of the triangle with vertices A(1,0,0), B(0,1,0) and C(0,0,1) is
- The volume of the parallelepiped with edges hat i+2hat j, hat j+3hat k and 2hat i+hat k is
- If |vec a|=3, |vec b|=4 and |vec a+vec b|=5, then the angle between vec a and vec b is
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