Vector has
A vector has both magnitude as well as direction.
Correct form of distributive law is
Distributive law is given by :
Magnitude of the vector
We have :
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
λ is a unit vector if and only if
is equal to
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
If P1(x1, y1, z1) and P2(x2, y2, z2) are any two points, then the vector joining P1 and P2is the vector P1P2, then ;
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).
The scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7) is given by : (- 5 – 2) i.e. – 7 and (7 – 1) i.e. 6. Therefore, the scalar components are – 7 and 6 .,and vector components are
Find a vector in the direction of the vector which has a magnitude of 8 units
Find , if
and
Direction angles are angles
α,β,γ are the angles which the position vector makes with the positive x-axis ,y-axis and z-axis respectively are called direction angles.
are any three vectors then the correct expression for distributivity of scalar product over addition is
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
Find a unit vector perpendicular to each of
It is given that:
Therefore, the unit vector perpendicular to both the vectors and
Direction cosines
Cosines of the angles α,β,γ are called direction cosines.
Magnitude of the vector
We have :
Find the sum of the vectors
and
We have:
Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.
Therefore, the D.C.’s of vector AB are given by:
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
If l , m and n are the direction cosines of vector then , the coordinates of point P are given by : lr ,mr and nr respectively.
Unit vectors along the axes OX, OY and OZ are denoted by
represents the unit vectors along the co ordinate axis i.e. OX ,OY and OZ respectively.
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
Let It is given that left|
, then ,
Putting these values in (1) , we get :
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