The direction cosines of the vector \(a=-2i+j-k\) are ?
\(\dfrac{2}{√6}, \dfrac{1}{√6},\dfrac{1}{√6}\)
\(\dfrac{-2}{√6}, \dfrac{1}{√6},\dfrac{-1}{√6}\)
\(\dfrac{-2}{√6}, \dfrac{-1}{√6},\dfrac{-1}{√6}\)
\(\dfrac{-2}{√6}, \dfrac{1}{√6},\dfrac{1}{√6}\)
\(\dfrac{-2}{√6}, \dfrac{-1}{√6},\dfrac{1}{√6}\)
The Correct Option is B
Solution and Explanation
Given that
\(a=-2i+j-k\) is a vector and we need to find the direction of Cosine of this vector
So we can proceed as
step1
\(|a|= √((-2)^{2}+1^{2}+(-1)^{2})\)
\(=\)\( √6\)
step 2
Direction of cosine of a vector are
\(\dfrac{-2}{√6}, \dfrac{1}{√6},\dfrac{-1}{√6}\) (Ans.)
Top Questions on Magnitude and Directions of a Vector
- The position vectors of two points P and Q are given by \(OP=2a-b\) and \(OQ=a+3b\) ,respectively.If a point R divides the line joining P and Q internally in the ratio \(1:2\) ,then the position vector of the point R is ?
- KEAM - 2023
- Mathematics
- Magnitude and Directions of a Vector
- The plane that is perpendicular to the planes \(x-y+2z-4=0\) and \(2x-2y+z=0\) and passes through \( (1,-2,1)\) is
- KEAM - 2023
- Mathematics
- Magnitude and Directions of a Vector
Let \(a=i+j+2k\) and \(b=i-2j+3k\) be two vectors. Then the unit vector in the direction of \(a-b\) is
- KEAM - 2023
- Mathematics
- Magnitude and Directions of a Vector
- Let x be a real number and a be any non-zero vector such \(|(4-x)a|<|3a|\).Then which of the following options is correct?
- KEAM - 2023
- Mathematics
- Magnitude and Directions of a Vector
- The value of \(λ\) for which the vectors \(i+j-k\)and \(λi+3j+k\) are perpendicular is ?
- KEAM - 2023
- Mathematics
- Magnitude and Directions of a Vector
Questions Asked in KEAM exam
- A Spherical ball is subjected to a pressure of 100 atmosphere. If the bulk modulus of the ball is 1011 N/m2,then change in the volume is:
- KEAM - 2023
- mechanical properties of solids
- Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
- KEAM - 2023
- System of Particles & Rotational Motion
- The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are
- KEAM - 2023
- Trigonometric Functions
- \(∫xlog(1+x^2)dx=\)?
- KEAM - 2023
- Integration by Parts
- A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
- KEAM - 2023
- System of Particles & Rotational Motion
Concepts Used:
Vectors
The quantities having magnitude as well as direction are known as Vectors or Vector quantities. Vectors are the objects which are found in accumulated form in vector spaces accompanying two types of operations. These operations within the vector space include the addition of two vectors and multiplication of the vector with a scalar quantity. These operations can alter the proportions and order of the vector but the result still remains in the vector space. It is often recognized by symbols such as U ,V, and W
Representation of a Vector :
A line having an arrowhead is known as a directed line. A segment of the directed line has both direction and magnitude. This segment of the directed line is known as a vector. It is represented by a or commonly as AB. In this line segment AB, A is the starting point and B is the terminal point of the line.
Types of Vectors:
Here we will be discussing different types of vectors. There are commonly 10 different types of vectors frequently used in maths. The 10 types of vectors are:
- Zero vector
- Unit Vector
- Position Vector
- Co-initial Vector
- Like and Unlike Vectors
- Coplanar Vector
- Collinear Vector
- Equal Vector
- Displacement Vector
- Negative of a Vector