Easy vector tutorial is process of tutoring to students in online by the tutors. Easy vector tutorial is the vectors which are specified by magnitude and direction. The examples of vectors are displacement, velocity, acceleration, momentum of force and weight. Easy vector tutorial is method tutoring on vector problems in the online with basic steps and calculations. Tutor vista is the main website to provide online tutors to give easy vector tutorial. The following problems are some of the examples of easy vector tutorial process done by tutor vista.
Easy vector tutorial on example problems
Example problem 1: Add 2`veci` +6`vecj`+4`veck` with 5`veci`+2`vecj`+2`veck`
Solution
Place the vectors according to the magnitudes shown below.
2`veci` + 6`vecj` +4`veck`
5`veci` + 2`vecj` +2`veck`
---------------------------
7`veci` + 8`vecj` + 6`veck`
----------------------------
Example problem 2: Subtract 5`veci` + 4`vecj`- 8`veck` with 4`veci`- 6`vecj` +3`veck`
Solution
Since we have the magnitudes in opposite direction it will be easy to perform method
(5`veci` + 4`vecj`- 8`veck`4`veci`- 6`vecj` +3`veck`
`(13 - 4)veci + (4-(-6))vecj + (-8-3)veck`
`(13 - 4)veci + (4 + 6))vecj + (-8-3)veck`
`9 veci +10vecj -11 veck`
Example problem 3: Find the magnitude of `2 veci - vecj + 7 veck`
Solution:
Magnitude of `2veci - 3vecj + 7 veck = |2veci - 3vecj + 7 veck|`
= `sqrt((2)^2 + (-3)^2 + (7)^2)`
`sqrt(4+9+49)`
=`sqrt (62)`
Example problem 4: Find the sum of the vectors `veca - vecb + 2 vecc` and `2veca +3vecb - 4vecc` and also find the modulus of the sum.
Solution
Let `vecx = veca - vecb + 2 vecc` , `vecy = 2veca + 3 vecb - 4vecc`
`vecx + vecy = (veca - vecb + 2 vecc) + (2veca + 3 vecb - 4vecc)`
`= 3 veca +2vecb - 2 vecc`
`|vecx + vecy| = sqrt (3^2 + 2^2 + (-2)^2)`
` = sqrt (9+4+4)`
` = sqrt 17`
Solution
Since we have the magnitudes in opposite direction it will be easy to perform method
(5`veci` + 4`vecj`- 8`veck`4`veci`- 6`vecj` +3`veck`
`(13 - 4)veci + (4-(-6))vecj + (-8-3)veck`
`(13 - 4)veci + (4 + 6))vecj + (-8-3)veck`
`(9) veci + (10)vecj + (-11) veck`
Example problem 3: Find the magnitude of `2 veci - vecj + 7 veck`
Solution:
Magnitude of `2veci - 3vecj + 7 veck = |2veci - 3vecj + 7 veck|`
= `sqrt((2)^2 + (-3)^2 + (7)^2)`
`sqrt(4+9+49)`
=`sqrt (62)`
Example problem 4: Find the sum of the vectors `veca - vecb + 2 vecc` and `2veca +3vecb - 4vecc` and also find the modulus of the sum.
Solution
Let `vecx = veca - vecb + 2 vecc` , `vecy = 2veca + 3 vecb - 4vecc`
`vecx + vecy = (veca - vecb + 2 vecc) + (2veca + 3 vecb - 4vecc)`
`= 3 veca +2vecb - 2 vecc`
`|vecx + vecy| = sqrt (3^2 + 2^2 + (-2)^2)`
` = sqrt (9+4+4)`
` = sqrt 17`
Easy vector tutorial on practce problems
1. Add 7`veca` +2`vecb`+3`vecc` with 2`veca`+3`vecb`+`3vecc`
Answer: 9`veca`+5`vecb`+6`vecc`
2. Subtract 4`veci` + 3`vecj`- 6`veck` with `veci`- 2`vecj` +2`veck`
Answer: `veci`+5`vecj` -8`veck`
3. Find the sum of the vectors `vecp -3 vecq + 2 vecr` and `3vecp +vecq - 2vecr` and also find the modulus of the sum.
Answer: 6
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