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Q.) 12. A, B, C and D have position vectors a, b, c and d, respectively, such that a - b = 2(d - c). Then
[A]
AB and CD bisect each other
[B]
BD and AC bisect each other
[C]
AB and CD trisect each other
[D]
BD and AC trisect each other
[A] AB and CD bisect each other
[B] BD and AC bisect each other
[C] AB and CD trisect each other
[D] BD and AC trisect each other
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Vector Algebra 📚
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 ...
4
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5
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6
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7
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8
ABCD is a parallelogram, and A1 and B1 are the midpoints of sides BC and CD, respectively. If AA1 + ...
9
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10
ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opp ...
11
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 ...
16
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 ...
18
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 ...
20
If the vectors a and b are linearly independent satisfying (√3 tan θ + 1) a + (√3 secθ - 2) b = 0, ...
21
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, ...
26
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
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