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Vector when added to the vector B equal to 3.0 ICAP 4.0 J cap is the resultant vector that in position while direction and has magnitude equal to the vector of them in the magnitude of vector of a?
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Vector when added to the vector B equal to 3.0 ICAP 4.0 J cap is the...
Explanation:

Given, vector B = 3.0i + 4.0j

Let vector A = xi + yj

Now, vector A + vector B = vector R (Resultant Vector)

Therefore, xi + yj + 3.0i + 4.0j = R

Combining like terms, (x+3)i + (y+4)j = R

Since we know that the magnitude of vector A is equal to the magnitude of vector R, we can set up an equation:

|A| = |R|

Using the formula for magnitude, we get:

|A| = √(x^2 + y^2) and |R| = √((x+3)^2 + (y+4)^2)

Setting these equal to each other:

√(x^2 + y^2) = √((x+3)^2 + (y+4)^2)

Squaring both sides:

x^2 + y^2 = (x+3)^2 + (y+4)^2

Expanding:

x^2 + y^2 = x^2 + 6x + 9 + y^2 + 8y + 16

Cancelling like terms:

6x + 8y = -25

Thus, any vector of the form xi + yj, where 6x + 8y = -25, when added to vector B, will result in a vector with the same magnitude as vector A.
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Vector when added to the vector B equal to 3.0 ICAP 4.0 J cap is the resultant vector that in position while direction and has magnitude equal to the vector of them in the magnitude of vector of a?
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