Hello candidate,

A vector refers to a physical quantity which has the value of both magnitude as well as direction which means that it can provide that information regarding both the magnitude as well as the point at which that specific quantity is heading towards. Here are the example of some specific vectors- displacement, velocity, acceleration, work, power, electromagnetic force, momentum, force, etc. are some of them.

Hope you found it helpful. If you have any further queries regarding any educational related doubts, feel free to post it here!!

Hello Aspirant,

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Good Luck!!

Any vector (directional entity) whose magnitude is 1(unit) is called unit vector.

Eg:- î is a unit vector along x axis

Hi.

In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square meter (W/m ² )

I hope this answers your query

Good Luck

Hello student.

These are the three forces mentioned in the question.

F1=3i-4j+2k

F2=2i+3j-k

F3=2i+4j-5k

Resultant of these forces in sum of these forces. So add up these three.

There by Resultant of these forces is F1+F2+F3

which is equal to (3i-4j+2k +(2i+3j-k )+(2i+4j-5k )

7i+3j-4k is the required answer

Hey

I suppose it will be like

A vector into B vector is (3*12)+(4*5)=36+20= 56

AB= root under (3 square+4 square) * root under (12 sqaure + 5 square)= 5+13=18

Hence mod of cos theta will be : 56/18= 3.11(which is not possible hence I guess you got the question wrong and it should have been either -4j cap or -5 j cap(one of these)).

Hello Aspirant

To find angle between two given vectors, we always use the dot product.

The dot product of two vectors is written as:

vector a.vector b = (mod of vector a)*(mod of vector b)*cos(theeta)

Now, a = 3icap + 4jcap, b = 12icap + 5jcap

So, we get vector a. vector b =  (3icap + 4jcap)*(12icap + 5jcap) = 36 + 20 = 56

Also, mod of a = square root(9 + 16) = 5

mod of b = square root(144 + 25) = 13

So, we get 56 = 13*5*cos(theeta)

cos(theeta) = 56/65

theeta = cos - inverse(56/65)

So, the angle between given vectors is cos - inverse(56/65).

Hi Candidate,

Vector calculus is the branch of Vector Mathematics which extends the notion of differentiation and integration in three dimensional space.

It is also referred as multi variable calculus which is used for Gravitational Field Problems, Electromagnetic Waves and othe fields which involves numerous dimensions of coordinate. The most important vector calculus includes topics such as Cartesian Formula, Plane and Line Geometry, and Vector Algebra.

Hope that this answer helps you.