If i - 3j + 5k bisec... - Vector Algebra

Countdown ⏱️x

Countdown ⏱️x

Q.) If i - 3j + 5k bisects the angle between a and -i + 2j + 2k, where a is a unit vector, then

[A]a = (41i + 88j - 40k)/105

[B]a = (41i + 88j + 40k)/105

[C]a = (-41i - 88j - 40k)/105

[D]a = (41i -88j - 40k)/105

Vector Algebra 📚

Four non-zero vectors will always be ...

A point O is the centre of a circle circumscribed about a triangle ABC. Then OA sin 2A + OB sin 2B ...

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 ...

If vectors AB = -3i + 4k and AC = 5i - 2j + 4k are the sides of a △ABC, then the length of the media ...

12. A, B, C and D have position vectors a, b, c and d, respectively, such that a - b = 2(d - c). The ...

Given three vectors a = 6i - 3j, b = 2i - 6j and c = -2i + 21j such that a = a + b + c. Then the re ...

If a + β + γ = a δ and β + γ + δ = αb, α and δ are non-collinear, then a + β + γ + δ equals ...

Given three non-zero, non-coplanar vectors a, b and c. r1 = pa + qb + c and r2 = a + pb + qc. If th ...

If the vectors a and b are linearly independent satisfying (√3 tan θ + 1) a + (√3 secθ - 2) b = 0, ...

If i - 3j + 5k bisects the angle between a and -i + 2j + 2k, where a is a unit vector, then ...

If 4i + 7j + 8k, 2i + 3j + 4k and 2i + 5j + 7k are the position vectors of the vertices A, B and C, ...

If b is a vector whose initial point divides the join of 5i and 5j in the ratio k:1 and whose termi ...

If x and y are two non-collinear vectors and ABC is a triangle with side lengths a, b and c satisfy ...

Let ABC be a triangle, the position vectors of whose vertices are respectively i + 2j + 4k, -2i + 2j ...

The position vectors of the points P and Q with respect to the origin O are a = i + 3j - 2k and b = ...

If a and b are two unit vectors and θ is the angle between them, then the unit vector along the ang ...

In triangle ABC, ∠A = 30°, H is the orthocenter and D is the midpoint of BC. Segment HD is produced ...

Let r1, r2, r3, ..., rn be the position vectors of points P1, P2, P3, ..., Pn relative to the origi ...

Vectors a = -4i + 3k and b = 14i + 2j - 5k are laid off from one point. Vector d, which is being la ...

Locus of the point P for which OP represents a vector with direction cosine cos α = 1/2 (where O is ...

A uni-modular tangent vector on the curve x = t^2 + 2, y = 4t - 5, z = 2t^2 - 6 at t = 2 is ...

ABCD is a parallelogram, and A1 and B1 are the midpoints of sides BC and CD, respectively. If AA1 + ...

Let us define the length of a vector a i + b j + c k as |a| + |b| + |c|. This definition coincides ...

Vectors a = i + 2j + 3k, b = 2i - j + k and c = 3i + j + 4k are so placed that the end point of one ...

A is a vector with direction cosines cos α, cos β and cos γ. Assuming the y-z plane as a mirror, th ...

Let a, b and c be three units vectors such that 3a + 4b + 5c = 0. Then which of the following state ...

If |a + b| < |a - b|, then the angle between a and b can lie in the interval ...

If G is the centroid of a triangle ABC, then GA + GB + GC is equal to ...

ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opp ...

In a trapezium, vector BC = α AD. We will then find that p = AC + BD is collinear with AD. If p = µ ...

Find the value of λ so that the points P, Q, R and S on the sides OA, OB, OC and AB, respectively, ...

I is the incenter of triangle ABC whose corresponding sides are a, b, c, respectively. a IA + b IB ...

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 ...

If x and y are two non-collinear vectors and a, b and c represent the sides of a △ABC satisfying (a ...