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Q.) If x and y are two non-collinear vectors and ABC is a triangle with side lengths a, b and c satisfying (20a - 15b)x + (15b - 12c)y + (12c - 20a)(x × y) = 0, then triangle ABC is
[A]
an acute-angled triangle
[B]
an obtuse-angled triangle
[C]
a right-angled triangle
[D]
an isosceles triangle
[A] an acute-angled triangle
[B] an obtuse-angled triangle
[C] a right-angled triangle
[D] an isosceles triangle
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Vector Algebra 📚
1
Four non-zero vectors will always be ...
2
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3
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5
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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 ...
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12. A, B, C and D have position vectors a, b, c and d, respectively, such that a - b = 2(d - c). The ...
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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 ...
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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 ...
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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 ...
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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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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
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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 ...
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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 ...
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Locus of the point P for which OP represents a vector with direction cosine cos α = 1/2 (where O is ...
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If x and y are two non-collinear vectors and ABC is a triangle with side lengths a, b and c satisfy ...
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