Represent graphically a displacement of 40km,30°east of north.
Represent graphically a displacement of 40km,30°east of north.
Solution and Explanation
Here,vector OP→ represents the displacement of 40km,30°East of North.
Top CBSE CLASS XII Mathematics Questions
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Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
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- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
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Top CBSE CLASS XII Vector Algebra Questions
Find the scalar components and magnitude of the vector joining the points\( P(x_{1},y_{1},z_{1})and Q(x_{2},y_{2},z_{2}).\)
If\( \vec{a}=\vec{b}+\vec{c}\), then is it true that |\(\vec{a}\)|=|\(\vec{b}\)|+|\(\vec{c}\)| ? justify your answer.
Find the value of \(x\) for which\( x(\hat{i}+\hat{j}+\hat{k})\)is a unit vector.
If \(\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=2\hat{i}-\hat{j}+3\hat{k}\) and \(\vec{c}=\hat{i}-2\hat{j}+\hat{k}\),find a unit vector parallel to the vector \(2\vec{a}-\vec{b}+3\vec{c}.\)
A girl walks \(4km\) towards west,then she walk \(3km\) in a direction \(30°\)east of north and stops.Determine the girls displacement from her initial point to departure.
Top CBSE CLASS XII Questions
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Concepts Used:
Types of Vectors
In general, vectors are used in Maths and Science and are categorized into 10 different types of vectors such as:-
- Unit Vector - When a vector has a magnitude of 1 unit length, called a Unit Vector.
- Co-Initial Vector - Two or more vectors that have the same initial point are known to be Co-Initial Vectors.
- Coplanar Vector - Vectors that lie either in the same plane or are parallel to the same plane are called Coplanar vectors.
- Equal Vector - When two vectors have equal direction as well as magnitude, they are Equal Vectors, even if the initial point is different for both vectors.
- Negative of a Vector - When two vectors have the same magnitude but have exactly different directions.
- Zero Vector - When a vector has the same starting and ending point and has zero magnitudes is called a zero vector. The starting point needs to coincide with the terminal point. It is denoted by 0. It is also known as the null vector.
- Position Vector - A vector that indicates the location or the position of a point in a plane (three-dimensional Cartesian system) w.r.t. its origin. If A is a reference origin and there’s an arbitrary point B in the plane then AB will be called the position vector of the point.
- Like and Unlike Vectors - Like vectors are the vectors that have the same direction. And unlike vectors are the vectors that have opposite directions.
- Collinear Vector - Vectors either lying in the same line or which are parallel to the same line are Collinear vectors.
- Displacement Vector - The vector AB will be known as a displacement vector if a point is displaced from position B to position A.