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Answer:
l = 6 inches
Step-by-step explanation:
We have,
The volume of a rectangular prism with a square base is .
Height of the prism is 5 in
It is required to find the length of the edge of the square base. Let it is l.
The formula of the volume of the rectangular prism is given by :
A is area of base of prism
It has a square base, l =b
So, the length of the edge of the square base is 6 inches.
Using the determinant method, the cross product is
so the answer is B.
Or you can apply the properties of the cross product. By distributivity, we have
(3i + 8j - 6k) x (-4i - 2j - 3k)
= -12(i x i) - 32(j x i) + 24(k x i) - 6(i x j) - 16(j x j) + 12(k x j) - 9(i x k) - 24(j x k) + 18(k x k)
Now recall that
- (i x i) = (j x j) = (k x k) = 0 (the zero vector)
- (i x j) = k
- (j x k) = i
- (k x i) = j
- (a x b) = -(b x a) for any two vectors a and b
Putting these rules together, we get
(3i + 8j - 6k) x (-4i - 2j - 3k)
= -32(-k) + 24j - 6k + 12(-i) - 9(-j) - 24i
= (-12 - 24)i + (24 + 9)j + (32 - 6)k
= -36i + 33j + 26k