Find the Length -3i-4j

Problem

∥−3*i−4*j∥

Solution

1. Identify the components of the vector. The vector is given in terms of unit vectors i and j as v=−3*i−4*j which corresponds to the coordinates (x,y)=(−3,−4)

2. Apply the formula for the magnitude (length) of a 2D vector, which is ∥v∥=√(,x2+y2)

3. Substitute the values into the formula:

∥v∥=√(,(−3)2+(−4)2)

4. Simplify the squares inside the square root:

∥v∥=√(,9+16)

5. Calculate the sum and the square root:

∥v∥=√(,25)

∥v∥=5

Final Answer

∥−3*i−4*j∥=5

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