help@askiitians.com

1800-150-456-789

Mechanics> what is the sum in unit-vector notation o...

question mark

what is the sum in unit-vector notation of two vectors a=5i+3j & b=-3i+2j? what are the magnitude & direction of a+b ?

Muhammad Mansoor Sarfraz , 7 Years ago

Grade 12th pass

2 Answers

Aryan Vartak

Last Activity: 7 Years ago

a = 5i + 3jb = -3i + 2jDirection of vector:a + b = [5+(-3)]i + [3+2]j = [5-3]i + [3+2]j = 2i + 5jIf you draw it on Cartesian co-ordinate system, it will have a positive gradient and will be going in a "North-east" directionModulus of vector:|a + b| = √[(2^2) + (5^2)] = √[4 + 25] = √29

Arun

Last Activity: 7 Years ago

Dear Sarfraz

Consider two vectors given as:

Then the sum (say $\overrightarrow{c}$ ) of the above two vectors can be stated in unit vector notation as:

Given:

(a) From above it is clear that the sum of the vectors $\overrightarrow{a}$ and vector $\overrightarrow{b}$ can be given in the unit vector notation as:
$\overrightarrow{c} = \overrightarrow{a} + \overrightarrow{b}$
Comparing the given vectors to the vectors represented by equation (1) and (2), we have
Therefore the sum of the vectors in unit vector notation is .

Therefore the sum of the vectors in unit vector notation is $2\widehat{i} + 5\widehat{j}$ .

Regards

Arun (askIITians forum expert)

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

question mark

A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat the free end, where a small mass of 2 g is positioned. determine(i) The velocity of the end when passing through the zero position(ii) The acceleration at maximum displacement(iii) The maximum kinetic energy of the mass

Mechanics

2 Answer Available

Last Activity: 2 Year ago(s)

question mark

An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of springconstant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by thedamping constant b = 0.07kg/s.(i) Find the period of the damped oscillation.(ii) By what percentage does the amplitude of the oscillation decrease in each cycle?

Mechanics

1 Answer Available

Last Activity: 2 Year ago(s)

question mark

If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0

Mechanics

1 Answer Available

Last Activity: 2 Year ago(s)

question mark

A particle is traveling in a circle of radius R =2.5m and with an angular velocity of 10 rad/s. What is the centripetal acceleration of the particle? The particle begins to slow down with an angular acceleration of -1 rad/s2. After 5 seconds, what is the centripetal acceleration and the tangential acceleration fo the particle?

Mechanics

1 Answer Available

Last Activity: 2 Year ago(s)

question mark

If the acceleration of block A is 5 m/s^2Find the acceleration of block B

Mechanics

1 Answer Available

Last Activity: 2 Year ago(s)

View all Questions