Vector 1 points along the z axis and has magnitude V1 = 80. Vector 2 lies in the xz plane, has magnitude V2 = 50, and makes a -37° angle with the x axis (points below the x axis). What is the scalar product V1·V2?
Question
Question
Vector 1 points along the z axis and has magnitude V1 = 80. Vector 2 lies in the xz plane, has magnitude V2 = 50, and makes a -37° angle with the x axis (points below the x axis). What is the scalar product V1·V2?
Answer:
[tex]\vec{V1}[/tex] . [tex]\vec{V2}[/tex] = 2574.08
Explanation:
given data
magnitude V1 = 80
magnitude V2 = 50
angle a = -37°
solution
[tex]\vec{V1}[/tex] = 80 k
[tex]\vec{V2}[/tex] = 50 cos{37} i – 50sin{37} k
so that here [tex]\vec{V1}[/tex] . [tex]\vec{V2}[/tex] is
[tex]\vec{V1}[/tex] . [tex]\vec{V2}[/tex] = 80 k . ( 50 cos{37} i – 50sin{37} k )
[tex]\vec{V1}[/tex] . [tex]\vec{V2}[/tex] = 80 k . ( 38.270 i + 32.176 k )
[tex]\vec{V1}[/tex] . [tex]\vec{V2}[/tex] = 2574.08