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# Dot Product and Angle Between Two Vectors (Grades 11-12)

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## Dot Product and Angle Between Two Vectors

1.
Find the dot product of the given vectors.
$<< 8,4 >> " & " << -7, -9 >>$
1. 20
2. -92
3. 92
4. -20
2.
Find the dot product of $vecy$ and $vecx$ if $vec y = <<-3, 12>>$ and $vec x =<<-8, -2>>$.
1. 48
2. 0
3. -20
4. 10
3.
Find the dot product of the given vectors.
$vecu=-veci+5vecj$
$vecv=-6veci-2vecj$
1. 12
2. -16
3. 16
4. -4
4.
Find the dot product of the given vectors.
$vecu=<<3,9>>$
$vecv=<<6,5>>$
1. 63
2. 27
3. 23
4. 57
5.
Find the angle between the two vectors.
$<<3, 6>> " & " <<3, -8>>$
1. 142.87°
2. 122.62°
3. 132.88°
4. 150.03°
6.
Find the measure of the angle between the two vectors.
$<<-2, 2>>$
$<<8, -1>>$
1. 135.6°
2. 122.2°
3. 140.3°
4. 142.1°
7.
Find the angle between the two vectors.
$vecu=-8vecj$
$vecv=-9veci-2vecj$
1. 77.47°
2. 86.42°
3. 74.87°
4. 68.92°
8.
Are these two vectors parallel, orthogonal, or neither?
$<<4, -9>> " & " <<-9, 4>>$
1. parallel
2. orthogonal
3. neither
9.
Are these two vectors parallel, orthogonal, or neither?
$vec u=-5veci-2vecj$
$vecv=-10veci+25vecj$
1. parallel
2. orthogonal
3. neither
10.
Find the angle between the vectors $vec(HE) and vec(HK)$.
1. 49.6°
2. 154.5°
3. 86.8°
4. 35.7°
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