Solve for v v=-2i-2j

Problem

v=−2*i−2*j

Solution

1. Identify the vector components from the given expression in terms of unit vectors i and j

2. Determine the magnitude of the vector using the formula |v|=√(,x2+y2)

|v|=√(,(−2)2+(−2)2)

|v|=√(,4+4)

|v|=√(,8)=2√(,2)

3. Calculate the direction angle θ using the formula tan(θ)=y/x noting that the vector lies in the third quadrant.

tan(θ)=(−2)/(−2)=1

θ=180+45=225

4. Represent the vector in component form.

v=<−2,−2>

Final Answer

v=<−2,−2>

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