Test: Vector Algebra- 1 - JEE

Find the unit vector in the direction of vector  where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively

If  is a non zero vector of magnitude ‘a’ and λ a non zero scalar, then λ is a unit vector if

Find the values of x and y so that the vectors  are equal

If P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂) are any two points, then the vector joining P1 and P2is the vector P1P2. Magnitude of the vector 

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7). 

Find a vector in the direction of the vector  which has a magnitude of 8 units

Find , if   and  

Direction angles are angles

 are any three vectors then the correct expression for distributivity of scalar product over addition is

Find the values of x and y so that the vectors 

Find the direction cosines of the vector 

Direction cosines

Magnitude of the vector 

Find the sum of the vectors    and  

Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

If a unit vector makes angles π/3 with   and an acute angle θ with  then find θ

If l, m and n are direction cosines of the position vector OP the coordinates of P are

Unit vectors along the axes OX, OY and OZ are denoted by 

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

Find the angle between two vectors  with magnitudes and 2, respectively, having 

If a unit vector  makes angles and an acute angle θ with , then the components of  are