Vectors properties pdf

It is known to us that there are two sorts of physical quantities namely scalars and vectors. Let us begin with the dot and cross product of vectors. Also read about Determinants here. The numbers lr, mr, and nr, proportional to the direction cosines are termed as direction ratios of vectors and denoted as a, b and c, respectively. A vector with magnitude r , direction ratios a, b, c , and direction cosines l, m, n of the vector are associated as:.

Learn more about Sets here. Consider X and Y to be two points concerning the origin O. Then the line segment connecting the points P and Q may be divided by a third point, say R, in two fashions; internally and externally. The direction of the vector can be the same or opposite to that of line m, depending upon the value of the angle. Geometrically, this represents the volume of the parallelepiped whose edges are of length x, y and z.

Know more about the Complex Numbers here. In the introduction, we read the definitions of vector and scalar quantities. The only difference between scalars and vectors is that a scalar is a quantity that does not rely on the direction. However, a vector is a physical quantity that possesses magnitude as well as direction. The common examples of scalars are speed, distance, time, etc. These are generally real values followed by their units of measurements.

Popular examples of vectors are velocity, displacement, force, acceleration, etc. Scalars and Vectors Examples Scalar : Time as 7 hours, Speed as 80 mph, which do not symbolize any direction.

Vectors : Displacement as ft, velocity mph symbolizes the direction. Negative velocity and displacement signify that the object is going in the opposite direction.

Questions based on Vector Algebra come up often in various prestigious government exams some of them are as follows. Stay tuned to the Testbook app or visit the testbook website for more updates on such similar topics from mathematics, science, and numerous such subjects, and can even check the test series available to test your knowledge regarding various exams. Sign Up for Free Already have an account? Sign In. Open in App Create free Account. Search for:. Get Pass Pass. Home » Maths.

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Learn now! Get Started for Free Download App. Answer Detailed Solution Below Option 3 : Answer Detailed Solution Below Option 2 : [a b c].

One Two Three Four. Concept: Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.

Answer Detailed Solution Below Option 1 : 1. Answer Detailed Solution Below Option 3 : 2. Concept: In an equilateral triangle, the centroid, orthocenter, Incenter all lie on same point. Incentre: Intersection of internal angle bisectors of the triangle. Circumcentre: Intersection of perpendicular bisectors of the triangle. To find: which statement is correct? The vectors are parallel The vectors are perpendicular The vectors are anti-parallel The vectors must be unit vectors.

Answer Detailed Solution Below Option 3 : - 2. Answer Detailed Solution Below Option 2 : a 2. Concept: Coplanar Vectors: All the vectors that lie on same plane or parallel to same plane.

In case of n vectors, if no more than two vectors are linearly independent, then all are coplanar.