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In this lesson, we will learn how to solve operations on vectors algebraically such as vector addition, vector subtraction, and scalar multiplication.

Q1:

Given that β π΄ = ( 0 , 1 ) and β π΅ = ( β 3 , β 6 ) , find 3 2 οΊ β π΄ β β π΅ ο .

Q2:

Given that β π΄ = ( 0 , β 1 ) and β β π β π΄ β β = 1 2 , find the possible values of π .

Q3:

Given that β π΄ = ( 2 , β 4 ) and β π΅ = ( β 7 , β 6 ) , find β π΄ β 4 β π΅ .

Q4:

A force of newtons is being applied to an object. What other force should be applied to achieve a total force of newtons?

Q5:

Given that u = β¨ 0 , 4 β© and v = β¨ 0 , β 5 β© , find the components of u v + .

Q6:

Given that u = β¨ 2 , β 3 β© , v = β¨ β 5 , 4 β© , and w = β¨ 3 , β 1 β© , find the components of u v w + + .

Q7:

Given that u = β¨ 2 , β 3 β© , v = β¨ 3 , 2 β© , and w = β¨ β 1 , β 5 β© , find the components of u v w + + .

Q8:

Given that u = β¨ 2 , β 4 β© and v = β¨ 0 , 0 β© , find the components of u v + .

Q9:

Shown on the grid of unit squares are the vectors u , v , and u v + .

What are the components of u ?

What are the components of v ?

What are the components of u v + ?

Q10:

The figure shows a regular hexagon π΄ π΅ πΆ π· πΈ πΉ divided into 6 equilateral triangles. Which of the following is equal to οͺ π΅ πΈ + ο« πΉ π΄ ?

Q11:

Given that u = β¨ 2 , β 4 β© and v = β¨ β 2 , 4 β© , find the components of u v + .

Q12:

Given that u = β¨ β 3 , β 1 β© , and v = β¨ β 2 , 5 β© , find the components of u v + .

Q13:

Given that u = β¨ 3 , 1 β© and v = β¨ 2 , 5 β© find the components of u + v .

Q14:

and Find .

Q15:

On a lattice, where ο π΄ πΆ = ( β 5 , β 5 ) , ο π΅ πΆ = ( β 1 2 , 6 ) , and 3 β πΆ + ο π΄ π΅ = ( β 8 , 1 3 ) , determine the coordinates of the point π΅ .

Q16:

On a lattice, where ο π΄ πΆ = ( 3 , 3 ) , ο π΅ πΆ = ( 1 3 , β 7 ) , and 2 β πΆ + 2 ο π΄ π΅ = ( β 4 , β 4 ) , find the coordinates of the point πΆ .

Q17:

Given that β π΄ = ( β 4 , β 1 ) and β π΅ = ( β 2 , β 1 ) , express β πΆ = ( β 8 , β 1 ) in terms of β π΄ and β π΅ .

Q18:

If β π΄ = ( 1 , 2 , 1 ) , β π΅ = ( β 1 , β 1 , 0 ) , and β πΆ = ( β 2 , β 1 , 1 ) , express β πΆ in terms of β π΄ and β π΅ .

Q19:

When is it true that u v v u + = + ?

Q20:

When is it true that β + β = β β + β β u v u v ?

Q21:

β π and ο π are two vectors, where β π = ( β 1 , 5 , β 2 ) and ο π = ( 3 , 1 , 1 ) . Comparing β β β π + ο π β β and β β β π β β + β β ο π β β , which quantity is larger?

Q22:

Find all the possible values of π given β π΄ = ( β 4 , 3 , 1 ) , β π΅ = ( 6 , β 6 , π β 1 3 ) and β β β π΄ + β π΅ β β = 7 .

Q23:

Given that β π΄ = ( 3 , 3 ) and β π΅ = ( 4 , 6 ) , find 1 2 οΊ β π΄ + β π΅ ο .

Q24:

Given that β π΄ = ( β 9 , 4 ) and β π΅ = ( 3 , β 2 ) , find β 1 2 οΊ β π΄ + β π΅ ο .

Q25:

Given that β π΄ = ( β 7 , 6 ) and β π΅ = ( 9 , β 7 ) , find 3 2 οΊ β π΄ β β π΅ ο .

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