find the triple scalar product u . (v * w) for the vectors
u = 9i - 7j - 3k
v = -6i + j - 5k
w = 2i + 8j - 9k
a. -877
b. -299
c. -19
d. 0
e. 899
look at
http://www.jiskha.com/display.cgi?id=1472551803
Make any changes necessary.
Also consider Steve's method if you have learned about determinants.
To find the triple scalar product u . (v * w), we need to follow these steps:
Step 1: Calculate the cross product of vectors v and w, denoted as (v * w).
Step 2: Take the dot product of vector u with the cross product result (v * w).
Let's calculate each step:
Step 1: Calculating the cross product (v * w):
(v * w) = (v2w3 - v3w2)i - (v1w3 - v3w1)j + (v1w2 - v2w1)k
Using the values given:
v = -6i + j - 5k
w = 2i + 8j - 9k
(v * w) = ((j * (-9) - (-5) * 8)i - ((-6) * (-9) - (-5) * 2)j + ((-6) * 8 - j * (-9))k
= (-9j - 40i - 57k)
Step 2: Calculating the dot product u . (v * w):
u = 9i - 7j - 3k
u . (v * w) = (9i - 7j - 3k) . (-9j - 40i - 57k)
= 9 * (-40) + (-7) * (-9) + (-3) * (-57)
= -360 + 63 + 171
= -126
So, the triple scalar product u . (v * w) is -126.
Among the answer choices provided:
a. -877
b. -299
c. -19
d. 0
e. 899
None of the answer choices matches the result we found, so the correct answer is not among the options provided.