Find the angle between vectors v and w. Find the projection p of v onto w. Calcu

Question

Find the angle between vectors v and w. Find the projection p of v onto w. Calculate the component of v onto w using the formula . Calculate |p| and discuss how this answer relates to your work in the last part. Let . Also, vector v has a direction angle of 150degree and a magnitude of 2. The vector u shown below is in the opposite direction from w. The vector q originates from the terminal point of v and terminates at the terminal point of u. so that q and u are orthogonal. Calculate the horizontal and vertical components of vector u. What is u called? Calculate the horizontal and vertical components of vector q. The vector q is called the component^1 of v onto w and is usually denoted orth_w v.

Explanation / Answer

3. v= (-3sqrt2 , 6) ; w = (2, 5sqrt5)

Angle between v and w = <v.w>/|v|*w|

<v,w> = -6sqrt2 +30sqrt5 = 58.59

|v| = sqrt( 18 +36) =sqrt54 = 7.35 ; |w| = sqrt(4+125) =11.36

Angle between v and w = 58.59/(7.35*11.36) = cos^-10.707 = 45.4 degrees

b) proj p i.e v onto w ={ <v.w>/||w||^2}w

={ 58.59/129}{2, 5sqrt5}

= 0.454(2, 5sqrt5)

= (0.908 , 5.07)

c) Vw = |v|cosangle = 7.35*cos45.4 = 5.16

d) |p| = 5.15

Both values are same and different way of calculating

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