Calculate the given quantity if u = i + j − 4k v = 3i − 5j + k w = j − 3k.

Question

Calculate the given quantity if

u = i + j − 4k    v = 3i − 5j + k    w = j − 3k.

(a)    2u + 3v

 

(b)    |u|

 

(c)    u · v

 

(d)    u × v

 

(e)    |v × w|

 

(f)    u · (v × w)

 

(g)    the angle between u and v (rounded to the nearest degree)

Answer 1

Kyle,

a) is not tough- 1i + 2j + 3k + 4i + 5j + 6k = 5i + 7j + 9k

b) this is asking for the magnitude of the vector, visually, this is length of the segment from (0,0,0) to (1,1,-4)

c) is not tough, but if it is tough, then you haven't seen dot products, and you should be able to learn how to find one quickly: 1i + 2j + 3k (dot) 4i + 5j + 6k = 4 + 10 + 18 = 32

d) if you have done determinants of 3x3 matrices, this is the same process

e) this is the magnitude of the vector, so visually speaking, this is the length

f) dot product--see above

g) there is a simple way to relate the dot product of a vector and the angle between the vectors -- you can find this easily in your textbook (a) dot (b) = product of the magnitudes times cos(angle between them)

hope this helps,--Andrew