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konstantin123 [22]
3 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]3 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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