Recall that for 3 vectors 
, all in 
, the vector triple product
So
Also recall the scalar triple product,
which gives the signed volume of the parallelipiped generated by the three vectors . When either 
or 
, the parallelipepid is degenerate and has 0 volume, so
and the above reduces to
so that
![(u\times v)\cdot[(v\times w)\times(w\times u)]=(u\times v)\cdot((v\times w)\cdot u)w](https://tex.z-dn.net/?f=%28u%5Ctimes%20v%29%5Ccdot%5B%28v%5Ctimes%20w%29%5Ctimes%28w%5Ctimes%20u%29%5D%3D%28u%5Ctimes%20v%29%5Ccdot%28%28v%5Ctimes%20w%29%5Ccdot%20u%29w)
The scalar triple product has the following property:
Since 
is a scalar, we can factor it out to get
and by the property above we have
and so we end up with
![[u\cdot(v\times w)]^2](https://tex.z-dn.net/?f=%5Bu%5Ccdot%28v%5Ctimes%20w%29%5D%5E2)
as required.
Answer:
B) 103.25
Step-by-step explanation:
Area of rectangle:
A = bh
A = (16)(4)
A = 64
Area of a semi-circle:
r = d/2 = 5
A = (πr²)/2
A = (3.14 * 5²)/2
A = (3.14 * 25)/2
A = (78.5)/2
A = 39.25
Combined:
64 + 39.25 = 103.25
Answer:
y = 3/-1 + 1 or y = -3/1 + 1
Step-by-step explanation:
Step-by-step explanation:
This is the answer of this question.
Answer:
-5
Step-by-step explanation:
3 minus 8 equals -5
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