1
Four non-zero vectors will always be ...
2
Let a, b and c be three units vectors such that 3a + 4b + 5c = 0. Then which of the following state ...
3
Let ABC be a triangle, the position vectors of whose vertices are respectively i + 2j + 4k, -2i + 2j ...
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If |a + b| < |a - b|, then the angle between a and b can lie in the interval ...
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A point O is the centre of a circle circumscribed about a triangle ABC. Then OA sin 2A + OB sin 2B ...
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If G is the centroid of a triangle ABC, then GA + GB + GC is equal to ...
7
If a is a non-zero vector of modulus a and m is a non-zero scalar, then m a is a unit vector if ...
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ABCD is a parallelogram, and A1 and B1 are the midpoints of sides BC and CD, respectively. If AA1 + ...
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The position vectors of the points P and Q with respect to the origin O are a = i + 3j - 2k and b = ...
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ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opp ...
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If vectors AB = -3i + 4k and AC = 5i - 2j + 4k are the sides of a △ABC, then the length of the media ...
12
12. A, B, C and D have position vectors a, b, c and d, respectively, such that a - b = 2(d - c). The ...
13
If a and b are two unit vectors and θ is the angle between them, then the unit vector along the ang ...
14
Let us define the length of a vector a i + b j + c k as |a| + |b| + |c|. This definition coincides ...
15
Given three vectors a = 6i - 3j, b = 2i - 6j and c = -2i + 21j such that a = a + b + c. Then the re ...
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If a + β + γ = a δ and β + γ + δ = αb, α and δ are non-collinear, then a + β + γ + δ equals ...
17
In triangle ABC, ∠A = 30°, H is the orthocenter and D is the midpoint of BC. Segment HD is produced ...
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Let r1, r2, r3, ..., rn be the position vectors of points P1, P2, P3, ..., Pn relative to the origi ...
19
Given three non-zero, non-coplanar vectors a, b and c. r1 = pa + qb + c and r2 = a + pb + qc. If th ...
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If the vectors a and b are linearly independent satisfying (√3 tan θ + 1) a + (√3 secθ - 2) b = 0, ...
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In a trapezium, vector BC = α AD. We will then find that p = AC + BD is collinear with AD. If p = µ ...
22
Vectors a = i + 2j + 3k, b = 2i - j + k and c = 3i + j + 4k are so placed that the end point of one ...
23
Vectors a = -4i + 3k and b = 14i + 2j - 5k are laid off from one point. Vector d, which is being la ...
24
If i - 3j + 5k bisects the angle between a and -i + 2j + 2k, where a is a unit vector, then ...
25
If 4i + 7j + 8k, 2i + 3j + 4k and 2i + 5j + 7k are the position vectors of the vertices A, B and C, ...
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If b is a vector whose initial point divides the join of 5i and 5j in the ratio k:1 and whose termi ...
27
Find the value of λ so that the points P, Q, R and S on the sides OA, OB, OC and AB, respectively, ...
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I is the incenter of triangle ABC whose corresponding sides are a, b, c, respectively. a IA + b IB ...
29
Let x^2 + 3y^2 = 3 be the equation of an ellipse in the x-y plane. A and B are two points whose pos ...
30
Locus of the point P for which OP represents a vector with direction cosine cos α = 1/2 (where O is ...
31
If x and y are two non-collinear vectors and ABC is a triangle with side lengths a, b and c satisfy ...
32
A uni-modular tangent vector on the curve x = t^2 + 2, y = 4t - 5, z = 2t^2 - 6 at t = 2 is ...
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If x and y are two non-collinear vectors and a, b and c represent the sides of a △ABC satisfying (a ...
34
A is a vector with direction cosines cos α, cos β and cos γ. Assuming the y-z plane as a mirror, th ...
