0

Guest

Courses New

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 ?

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 ?
 

Grade:12th pass

2 Answers

Aryan Vartak
24 Points
6 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
25750 Points
6 years ago
Dear Sarfraz
 
 
Consider two vectors given as:
232-1862_50.PNG
Then the sum (say \overrightarrow{c}) of the above two vectors can be stated in unit vector notation as:
232-1572_51.PNG
Given:
232-2286_52.PNG
(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 .
232-2190_53.PNG
Therefore the sum of the vectors in unit vector notation is 2\widehat{i} + 5\widehat{j}.
232-2385_54.PNG232-1270_55.PNG
 
Regards
Arun (askIITians forum expert)

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More