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A vector has both magnitude as well as direction.
Distributive law is given by :
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
If P_{1}(x_{1}, y_{1}, z_{1}) and P_{2}(x_{2}, y_{2}, z_{2}) are any two points, then the vector joining P1 and P2is the vector P1P2. Magnitude of the vector
If P_{1}(x_{1}, y_{1}, z_{1}) and P_{2}(x_{2}, y_{2}, z_{2}) 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
α,β,γ are the angles which the position vector makes with the positive xaxis ,yaxis and zaxis 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 :
It is given that:
Therefore, the unit vector perpendicular to both the vectors and
Cosines of the angles α,β,γ are called direction cosines.
We have :
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.
represents the unit vectors along the co ordinate axis i.e. OX ,OY and OZ respectively.
Write down a unit vector in XYplane, making an angle of 30° with the positive direction of xaxis.
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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