Archive for the ‘vectors’ Category

Problem 764

What are the projection of the point (-2,3,10)on the coordinate planes?

On the x y – plane: ( __,__ ,__)

On the y z – plane: (__, __ ,__ )

On the x z- plane : (__ ,__ ,__)

 

Solution:-

 

On the x y – plane: (-2,3,0)

On the y z – plane: (0,0,10)

On the x z- plane : (-2,0,10)

 

Problem 653

Find the appropriate angle between the vectors.

u = (3, -5, 2), and (-9, 5, 1)

 

Solution:-

 

To find the angle we use the identity u\cdot v=\left | u \right |\left | v \right |cos\Theta .

cos\Theta =\frac{(\left | u \right |\left | v \right |)}{(u\cdot v)} =\frac{-50}{\sqrt{38}\sqrt{107}}

= \Theta \approx 2.47radians \approx 141^{\circ}

 

 

Problem 652

Compute the dot product of the vectors u and v.

u = (3, -5, 2), and (-9, 5, 1)

 

Solution:-

 

u .v = u1v1 + u2v2 + u3v3

Therefore u .v = (3)*(-9)+(-5)(5)+(2)(1)

= -27 – 25 + 2

= -50.