53.1k views
4 votes
If v= 5i-5j and w= xi+6j, find all numbers c for which | v+w| = 3

User Kiyan
by
8.1k points

1 Answer

5 votes

Answer: To find the values of "c" for which |v + w| = 3, we need to first calculate v + w and then find the magnitude (or length) of the resulting vector.

Given:

v = 5i - 5j

w = xi + 6j

Let's find v + w:

v + w = (5i - 5j) + (xi + 6j)

Now, combine like terms:

v + w = (5 + x)i + (6 - 5)j

v + w = (5 + x)i + j

Now, to find the magnitude of v + w, we use the formula:

|v + w| = √((5 + x)^2 + 1^2)

We want |v + w| to be equal to 3:

√((5 + x)^2 + 1^2) = 3

Now, let's solve for "x":

(5 + x)^2 + 1 = 3^2

(5 + x)^2 + 1 = 9

(5 + x)^2 = 9 - 1

(5 + x)^2 = 8

Now, take the square root of both sides:

5 + x = ±√8

5 + x = ±2√2

Now, isolate "x" in each case:

5 + x = 2√2

x = 2√2 - 5

5 + x = -2√2

x = -2√2 - 5

So, there are two values of "c" for which |v + w| = 3:

c = 2√2 - 5

c = -2√2 - 5

User Audrey Dutcher
by
8.1k points

Related questions

asked Jul 19, 2020 26.9k views
Turi asked Jul 19, 2020
by Turi
8.3k points
2 answers
5 votes
26.9k views
2 answers
4 votes
214k views
asked Oct 15, 2020 39.6k views
Cymric asked Oct 15, 2020
by Cymric
8.6k points
1 answer
2 votes
39.6k views