Pls help I’ll brain-lest ASAP
1 answer:
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Answer:
Area = 13.15 square units
Step-by-step explanation:
Let the given vertices be represented as follows:
A(2, -1, 1) = 2i - j + k
B(5, 1, 4) = 5i + j + 4k
C(0, 1, 1) = 0i + j + k
D(3, 3, 4) = 3i + 3j + 4k
(i) Let's calculate the vectors of all the sides:
AB = B - A = (5i + j + 4k) - (2i - j + k)
AB = 5i + j + 4k - 2i + j - k [Collect like terms]
AB = 3i + 2j + 3k
BC = C - B = (0i + j + k) - (5i + j + 4k)
BC = 0i + j + k - 5i - j - 4k [Collect like terms]
BC = -5i + 0j - 3k
CD = D - C = (3i + 3j + 4k) - (0i + j + k)
CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]
CD = 3i + 2j + 3k
DA = A - D = (2i - j + k) - (3i + 3j + 4k)
DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]
DA = -i - 4j - 3k
AC = C - A = (0i + j + k) - (2i - j + k)
AC = 0i + j + k - 2i + j - k [Collect like terms]
AC = -2i + 2j
BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)
BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]
BD = -2i + 2j
(ii) From the results in (i) above, we can deduce that;
AB = CD This implies that AB || CD [AB is parallel to CD]
AC = BD This implies that AC || BD [AC is parallel to BD]
(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram
<u>Now let's calculate the area</u>
To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.
In this case, we'll choose AB and AC
Area = |AB X AC|
Where;
<u></u>
AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)
AB X AC = - 6i - 6j + 10k
|AB X AC| =
|AB X AC| =
|AB X AC| = 13.15
Area = 13.15 square units.
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<u></u>
<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.
Answer:
a) It takes 0.0017s for the light to reach San Francisco.
b) It takes 0.033s for the light to reach London.
c) It takes 1.334s for the light to reach Mars.
d) It takes 149.7s for the light to reach Venus.
Step-by-step explanation:
Here we can solve this problem by using this following formula:
In which s is the speed(in km/s), d is the distance(in km) and t is the time(in s).
The light speed is 299 792 458 m / s = 299,792.458 km/s, so
(a) San Francisco (about 500km)
Find t when . So
It takes 0.0017s for the light to reach San Francisco.
b) London(about 10,000km)
Find t when . So
It takes 0.033s for the light to reach London.
(c) the Moon (400,000km)
Find t when . So
It takes 1.334s for the light to reach Mars.
(d) Venus (0.3 A.U. from Earth at its closest approach).
Each A.U. has 149,59,7871 km.
So 0.3 A.U. = 0.3*(149,597,871) = 44,879,361.3. This means that . So:
It takes 149.7s for the light to reach Venus.