DESPERATELY need calculus help!!

Question

Q1) Find the magnitude of the vectors: 
a) (1,2,−2) 
b) (6,−3,2) 
c) (0.5,2,−4) 

Q2) Let u be the unit vector in the direction of AB when A is the point with co-ordinates (−1,2,2) and B is the point with co-ordinates (4,4,5). 

Give the vector u 

Q3) Let the points A,B,C and D have position vectors a=(2,3,1),b=(1,6,–5),c=(–2,0,4), and d=(–4,–4,10) with respect to the origin O. 

a) Is ABC a right-angled triangle? 
b) Are the points B,C and D collinear? 
c) Is OAC a right-angled triangle? 
d) Are the points A,C and D collinear? 


Q4) 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∣ 
b) Is a−b orthogonal to c? 
c) Find the following angles (in radians): AOB and BOC

Answer 1

c) From the pythagorean theorem

OAC is not a rightangle traingle.

d) The condition for collinear ( A C D ) = 0

Therefore, A,C and D are not collinear.

Answer 2

Q1)

Caliculate the magnitude of vector by using following formula

a) < 1, 2, -2 >

                                        

                                       

                                       

b) < 6, -3, 2 >

                                       

                                      

                                      

c) < 0.5, 2, - 4 >

                                        

                                       

                                       

Answer 3

Q2) A < - 1, 2, 2 >,  B < 4, 4, 5 >

Calculate

Calculate the unit vector by using fallowing formula.

Comments

Thank you this has been so much help! I just have one question. For question two, the answer is stated to just be three numbers with commas between them so would it just be 5,2,3. Is sqrt38 needed? It looks like this below.

 

( , ,  )

 

---

<5,2,4> is represents vector .

yes, sqrt 38 is magnitude.

Answer 4

Calculate the position vectors and magnitudes.

a) From the pythagorean theorem

ABC is not a right angle triangle.

b) The condition for collinear ( B C D ) = 0

Therefore, B,C and D are collinear.

Answer 5

Q4)

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.

            

            

Therefore, a-b orthogonal to c.

Answer 6

Q4)c) Angles AOB and BOC

Compute the angle by using following formula