JEE Advanced Level Test: Vector Algebra - JEE MCQ

Let be a vector perpendicular to , where  then (ℓ +m+n) is equal to 

If  are three non-coplaner non-zero vectors and is any vector in space, then    is equal to

If a, b, c are pth, qth, rth terms of an H.P and 

If the unit vectors are inclined at an angle 2θ and , then for θ ∈ [0, π], θ may lie in the interval 

Consider a tetrahedron with faces f₁, f₂, f₃, f₄ Let ​ be the vectors whose magnitudes are respectively equalt to the areas of  f₁, f₂, f₃, f₄ and  whose directions are perpendicular to these faces in the outward direction. Then

Let  be non-coplaner unit vectors equally inclined to one another at an acute angle θ. Then in terms of  θ is equalt to 

Let  and  .  If the vector   lies in the plane of  , then x equals 

Images of the point P with position vector  in the line whose vector equation is has the position vector

Let  be such that . If the projection is equal to that of  are  perpendicular  to each other, then  equals.

Let  and . If  is a unit vector such that  then  is equal to 

Equation of a line which passes through a point with position vector , parallel to the plane  and perpendicular to the line 

Points L, M and N lie on the sides AB, BC and CA of the triangle ABC such that ℓ(AL) : ℓ(LB) = ℓ(BM) :ℓ(MC) = ℓ(CN) : ℓ(NA) = m :n, then the areas of the triangles LMN and ABC are in the ratio 

 is equal to 

If the vectors  (a ≠ b ≠ c ≠ 1) are coplanar, then the value of  is equal to 

The vectors  are coinitial. The vector  which is bisecting the angle between the vectors  and is having the magnitude √6 is 

If A₁, A₂, A₃, .........A_n are the vertics of a regular plane polygon with n sides and O is its centre then  equals

For any four points P,Q, R, S,  is equal to 4 times the 

area of the triangle

If a line has a vector equation , then which of the following statements hold goods ?

The vector  is 

The vector  directed along the external bisector of the angle between the vectors  and  with 

Which of the following acts in accordance with right hand screw rule?