1
Four non-zero vectors will always be ...
Vector Algebra
2
Let a, b and c be three units vectors such that 3a + 4b + 5c = 0. The ...
Vector Algebra
3
Let ABC be a triangle, the position vectors of whose vertices are resp ...
Vector Algebra
4
If |a + b| < |a - b|, then the angle between a and b can lie in the i ...
Vector Algebra
5
A point O is the centre of a circle circumscribed about a triangle AB ...
Vector Algebra
6
If G is the centroid of a triangle ABC, then GA + GB + GC is equal to ...
Vector Algebra
7
If a is a non-zero vector of modulus a and m is a non-zero scalar, th ...
Vector Algebra
8
ABCD is a parallelogram, and A1 and B1 are the midpoints of sides BC ...
Vector Algebra
9
The position vectors of the points P and Q with respect to the origin ...
Vector Algebra
10
ABCD is a quadrilateral. E is the point of intersection of the line jo ...
Vector Algebra
11
If vectors AB = -3i + 4k and AC = 5i - 2j + 4k are the sides of a △ABC ...
Vector Algebra
12
12. A, B, C and D have position vectors a, b, c and d, respectively, s ...
Vector Algebra
13
If a and b are two unit vectors and θ is the angle between them, then ...
Vector Algebra
14
Let us define the length of a vector a i + b j + c k as |a| + |b| + | ...
Vector Algebra
15
Given three vectors a = 6i - 3j, b = 2i - 6j and c = -2i + 21j such t ...
Vector Algebra
16
If a + β + γ = a δ and β + γ + δ = αb, α and δ are non-collinear, th ...
Vector Algebra
17
In triangle ABC, ∠A = 30°, H is the orthocenter and D is the midpoint ...
Vector Algebra
18
Let r1, r2, r3, ..., rn be the position vectors of points P1, P2, P3, ...
Vector Algebra
19
Given three non-zero, non-coplanar vectors a, b and c. r1 = pa + qb + ...
Vector Algebra
20
If the vectors a and b are linearly independent satisfying (√3 tan θ ...
Vector Algebra
21
In a trapezium, vector BC = α AD. We will then find that p = AC + BD ...
Vector Algebra
22
Vectors a = i + 2j + 3k, b = 2i - j + k and c = 3i + j + 4k are so pl ...
Vector Algebra
23
Vectors a = -4i + 3k and b = 14i + 2j - 5k are laid off from one poin ...
Vector Algebra
24
If i - 3j + 5k bisects the angle between a and -i + 2j + 2k, where a ...
Vector Algebra
25
If 4i + 7j + 8k, 2i + 3j + 4k and 2i + 5j + 7k are the position vecto ...
Vector Algebra
26
If b is a vector whose initial point divides the join of 5i and 5j in ...
Vector Algebra
27
Find the value of λ so that the points P, Q, R and S on the sides OA, ...
Vector Algebra
28
I is the incenter of triangle ABC whose corresponding sides are a, b, ...
Vector Algebra
29
Let x^2 + 3y^2 = 3 be the equation of an ellipse in the x-y plane. A ...
Vector Algebra
30
Locus of the point P for which OP represents a vector with direction ...
Vector Algebra
31
If x and y are two non-collinear vectors and ABC is a triangle with s ...
Vector Algebra
32
A uni-modular tangent vector on the curve x = t^2 + 2, y = 4t - 5, z ...
Vector Algebra
33
If x and y are two non-collinear vectors and a, b and c represent the ...
Vector Algebra
34
A is a vector with direction cosines cos α, cos β and cos γ. Assuming ...
Vector Algebra
