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konstantin123 [22]
2 years ago
15

Let vector a = 3i + j - k. Find the vector b in the direction of vector a such that |b| = 5

Mathematics
1 answer:
Serjik [45]2 years ago
3 0

Answer:

5i +(5/3)j - (5/3)k

Step-by-step explanation:

Vector b is in the same direction as vector a, so it is a scalar multiple of a.

b = ca for some positive real number c.

b = c(3i + j - k) = 3ci + cj - ck

|b| = sqrt[(3c)^2 + c^2 - c^2] = sqrt(9c^2) = 3c

If |b| = 5, then 3c = 5 and c = 5/3

That makes b = (5/3)(3i + j - k) = 5i +(5/3)j - (5/3)k

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Karo-lina-s [1.5K]

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puteri [66]

If "a" and "b" are two values of x-coordinate, and "m" is the midpoint between them, it means the distance from one end to the midpoint is the same as the distance from the midpoint to the other end

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Solving for m gives

... m = (a+b)/2

This applies to y-coordinates as well. So ...

... The midpoint between (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2)

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Jennifer had (x1, y1) = (-4, 10) and (x2, y2) = (-2, 6). So her calculation would be

... midpoint = ((-4-2)/2, (10+6)/2) = (-6/2, 16/2) = (-3, 8)

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A man invests $2000 in an account that pays 6.5% interest per year, compounded quarterly.
skelet666 [1.2K]

Answer:

The correct answer is a. $2275.28; b. 17.04 years

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a. Time (t) for the investment is given to be 2 years.

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b. Now the value of A is given to be triple the principal = $ (3 × 2000).

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Therefore it would take 17.04 years for the principal to triple.

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3 years ago
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