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In this lesson, we will learn how to get the polar form of a vector and how to prove that the two vectors are parallel or perpendicular.

Q1:

If ο π π΄ = ( 7 , 6 0 ) β is the position vector, in polar form, of the point π΄ relative to the origin π , find the π₯ π¦ -coordinates of π΄ .

Q2:

If ο π πΆ = οΌ 4 β 3 , 3 π 4 ο is the position vector, in polar form, of the point πΆ relative to the origin π , find the π₯ π¦ -coordinates of the point πΆ .

Q3:

Trapezium π΄ π΅ πΆ π· has vertices π΄ ( 1 0 , 1 1 ) , π΅ ( π , 8 ) , πΆ ( 4 , β 1 2 ) , and π· ( β 2 , 6 ) . Given that ο π΄ π΅ β«½ ο πΆ π· , find the value of π .

Q4:

Given the point π΄ ο» β 4 β 3 , 4 ο , express, in polar form, its position vector relative to the origin point.

Q5:

Given the point π΄ ( β 5 , 5 ) , express, in polar form, its position vector relative to the origin point.

Q6:

Given the point π΄ ( 1 0 , 1 0 ) , express, in polar form, its position vector relative to the origin point.

Q7:

Given the point π΄ ο» 3 β 3 , β 9 ο , express, in polar form, its position vector relative to the origin point.

Q8:

Given the point π΄ ο» β 4 β 3 , β 1 2 ο , express, in polar form, its position vector relative to the origin point.

Q9:

Given that the vectors and are perpendicular, find the value of .

Q10:

Let and

Find .

Which of the following is, therefore, true of the vectors?

Q11:

Given that β π΄ = ( β 6 , β 1 5 ) , β π΅ = ( π , β 1 0 ) , and β π΄ β«½ β π΅ , find the value of π .

Q12:

Given that the vectors and are perpendicular, find the value of π₯ .

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