FLASH SALES
education

Vectors problem|How to solve vector in physics| how To prove; (I) A. [ B × C ] = B. [ C × A ] = C. [ A × B ], B. [ A × C ] = -A. [ B × C ] (III) and A. [ B × A ] = 0 is correct

Solving vector problem

Let’s solve maths(vectors)
Use A = 2i + 3j – 5k
B = 3i + j +2k
C = I – j + 3k
To prove;
(I) A. [ B × C ] = B. [ C × A ] = C. [ A × B ](II) B. [ A × C ] = -A. [ B × C ](III) A. [ B × A ] = 0 is correct
SOLUTIONS

Note: The coefficient of I, j and k are the ones multiplying themselves the I, j and k still remain the same. I.e alike factors multiply themselves


(I) A. [ B × C ] = B. [ C × A ] = C. [ A × B ]first we’ll solve for A. [ B × C ] then relate it to B. [ C × A ] after we’ll check if it’s true for C. [ A × B ]Let’s get down to business
Solve for A. [ B × C ]2i+3j-5k[ (3i +j+2k) × (i-j+3k) ]2i+3j-5k[ 3i×i +j×-j + 2k×3k ]2i+3j-5k[ 3i -j+6k ]2i × 3i + 3j×-j – 5k×6k
=6i -3j -30k

For B. (C × A)
3i+j+2k[ (i – j+3k) × (2i+3j-5k) ]3i+j+2k[ 2i-3j-15k ]3i×2i + j×-3j + 2k×-15k
=6i -3j -30k

For C. [A × B]i – j +3k [ (2i +3j -5k) × (3i + j +2k) ]i – j +3k [ 2i×3i +3j×j – 5k×2k ]i – j +3k [ 6i +3j – 10k ]i×6i – j×3j + 3k×-10k
= 6i -3j -30k
So therefore, A. [ B × C ] = B. [ C × A ] = C. [ A × B]

(2) ANSWER FOR QUESTION 2
(II) B. [ A × C ] = -A. [ B × C ]Solve first for B. [ A × C ]3i + j + 2k [ (2i + 3j – 5k) × (i – j + 3k) ]3i + j + 2k [ 2i – 3j – 15k ]3i×2i + j×-3j + 2k×-15k
= 6i -3j -30k
Then solve for right hand side
-A. (B × C)
-[2i+3j-5k] [ (3i +j+2k) × (i-j+3k) ]-2i-3j+5k[ 3i×i +j×-j + 2k×3k ]-2i-3j+5k[ 3i -j+6k ]-2i × 3i – 3j×-j + 5k×6k
=-6i +3j + 30k
So therefore B. [ A × C ] is not equal to -A. [ B × C ]

(3) ANSWER FOR QUESTION 3
(III) A. [ B × A ] = 0 is correct
As, A×B = ABsin theta
ABsin theta is a vector which is perpendicular to the plane having A vector and V vector which implies that it is also perpendicular to A vector.
And A = AB cos theta
NOTE: An angle is perpendicular only if it is 90°
Therefore,
A. [ B× A ] = AB cos theta. × AB son theta
Theta = 90°
= AB cos 90° × AB son 90°
= AB[0] × AB [1]Anything multiply by zero is what
Answer: sure it will be zero, so therefore it’s true

Invite your friends
YouTube link: https://youtube.com/channel/UC54N4VE0RrjjIkz2tSQWjXA

You can post your questions or solvings on any course via this website: emperorelectricalworks.com.ng
YouTube link: https://youtube.com/channel/UC54N4VE0RrjjIkz2tSQWjXA

Facebook group:. https://facebook.com/groups/205235433977492/

YouTube video

YOU CAN DO IT

Oluwamuyide Peter

On the 4th of November I officially became a member of the exclusive 1st student with distinction after five years of no such record, in the history of The Polytechnic Ibadan, Faculty of Engineering to graduate with distinction as a DPP students since its establishment in 2011. My unrelenting power to solve problems, have made me to create a platform where student can get valid information anywhere, anyplace at anytime Evolving education world wide 🌎

Related Articles

2 Comments

  1. Fantastic goods from you, man. I have understand
    your stuff previous to and you are just extremely great.
    I actually like what you’ve acquired here, certainly like what you are stating and the
    way in which you say it. You make it entertaining and you still care for to keep it smart.

    I cant wait to read much more from you. This is really a wonderful web site.

Leave a Reply

Back to top button