Calculus question

Question

Q1) A, B and C are points with position vectors a=(1,−1,−1),b=(−2,1,−1) and c=(0,0,2). 

a) Compute ∣a∣, ∣b∣ and ∣c∣ 

is lal √1^2 + (-1)^2 + (-1)^2  and so on

 

b) Is a−b orthogonal to c? 

What does this mean? Just perpendicular? 

c) Find the following angles (in radians): AOB and BOC

Answer 1

c) Angles AOB and BOC

Compute the angle by using following formula

Angle AOB

     

    

    

Angle BOC

Answer 2

a) Compute the magnitudes.

a < 1, -1, -1 >

   

  

b = < -2, 1, -1 >

   

  

c = < 0, 0, 2 >

  

 

 

 

b) If a and b are vectors whose dot product is zero are said to be orthogonal.

Orthogonal  means perpendicular

            

            

Therefore, a-b orthogonal to c.