Question

Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.v = (7i - 3j) - (10i - 3j)

Accepted Answer

First, simplify the given vector expression by subtracting the components of the vectors: $$v = (7\mathbf{i} - 3\mathbf{j}) - (10\mathbf{i} - 3\mathbf{j}). $$This means subtract the $$i$$ components and the $$j$$ components separately. Calculate the resulting vector components: $$v = (7 - 10)\mathbf{i} + (-3 - (-3))\mathbf{j}. $$Simplify these to find the components of $$v. $$Find the magnitude $$||v|| of $$the vector using the formula $$||v|| = \sqrt{v_x^2$ + v_y^2$}$$, where $$v_x$$ and $$v_y$$ are the $$i$$ and $$j$$ components of the vector respectively. Determine the direction angle $$	heta of $$the vector relative to the positive $$x-$$axis using the formula $$	heta = 	an$$^{-1}$$\left(\frac{v_y}{v_x}ight). $$Make sure to consider the quadrant in which the vector lies to find the correct angle. Convert the angle $$	heta$$ from radians to degrees if necessary, and round the magnitude to the nearest hundredth and the angle to the nearest tenth of a degree as requested.

Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.

v = (7i - 3j) - (10i - 3j)

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Concetti chiave

Vector Subtraction

Magnitude of a Vector

Direction Angle of a Vector