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In this lesson, we will learn how to recognize parallel and perpendicular lines in space.

Q1:

Which of the following vectors is not perpendicular to the line whose direction vector β π is ( 6 , β 5 ) ?

Q2:

In the figure, π΄ π» is perpendicular to the plane π , which contains the points π» , π΅ , πΆ , π· a n d . If π΅ π· = 3 6 and π΄ π· = 8 5 , find the area of β³ π΄ π΅ π· .

Q3:

Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are parallel.

Q4:

Given that , , and , find the relation between and .

Q5:

Given that ο π = β β π β 2 β π , β πΏ = π β π β 8 β π , and ο π β«½ β πΏ , where β π and β π are two perpendicular unit vectors, find the value of π .

Q6:

Suppose A = β¨ 1 , 3 , 2 β© , B = β¨ π , 9 , π β© , C = β¨ π , π , π + π β© , and A B β₯ , find | | C .

Q7:

Given the two vectors β π΄ = ο» 8 β π β 7 β π + β π ο and β π΅ = ο» 6 4 β π β 5 6 β π + 8 β π ο , determine whether these two vectors are parallel, perpendicular, or otherwise.

Q8:

Find the values of π and π so that vector 2 β π + 7 β π + π β π is parallel to vector 6 β π + π β π β 2 1 β π .

Q9:

Find the values of π and π so that vector 5 β π + 4 β π + π β π is parallel to vector 1 5 β π + π β π β 3 β π .

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