Answer the following as true or false.
(i)a→and -a→are collinear.
(ii)Two collinear vectors are always equal in magnitude.
(iii)Two vectors having same magnitude are collinear.
(iv)Two collinear vectors having the same magnitude are equal.
Answer the following as true or false.
(i)a→and -a→are collinear.
(ii)Two collinear vectors are always equal in magnitude.
(iii)Two vectors having same magnitude are collinear.
(iv)Two collinear vectors having the same magnitude are equal.
Solution and Explanation
(i)True Vectors a→and -a→are parallel to the same line.
(ii)False Collinear vectors are those vectors that are parallel to the same line.
(iii)False.
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}.
- Relation R in the set A={1,2,3,4,5,6} defined as R={(x,y): y is divisible by x}.
- 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
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
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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- A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is
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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.