Find a unit vector in the same direction as the given vector ( vec{v} = 3hat{i} - 4hat{j} + 2hat{k} ).

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Accepted Answer

Step:1 ：Step 1: Calculate the magnitude of the given vector. The magnitude of a vector ( vec{v} = ahat{i} + bhat{j} + chat{k} ) is given by ( sqrt{a^2 + b^2 + c^2} ). So, the magnitude of ( vec{v} ) is ( sqrt{3^2 + (-4)^2 + 2^2} = sqrt{9 + 16 + 4} = sqrt{29} ).Step:2 ：Step 2: Determine the unit vector in the same direction as ( vec{v} ). A unit vector in the same direction as a given vector ( vec{v} ) is given by ( frac{vec{v}}{||vec{v}||} ). So, the unit vector in the same direction as ( vec{v} ) is ( frac{3hat{i} - 4hat{j} + 2hat{k}}{sqrt{29}} = frac{3}{sqrt{29}}hat{i} - frac{4}{sqrt{29}}hat{j} + frac{2}{sqrt{29}}hat{k} ).

Answer

Step: 1 ：Step 1: Calculate the magnitude of the given vector. The magnitude of a vector ( vec{v} = ahat{i} + bhat{j} + chat{k} ) is given by ( sqrt{a^2 + b^2 + c^2} ). So, the magnitude of ( vec{v} ) is ( sqrt{3^2 + (-4)^2 + 2^2} = sqrt{9 + 16 + 4} = sqrt{29} ).Step: 2 ：Step 2: Determine the unit vector in the same direction as ( vec{v} ). A unit vector in the same direction as a given vector ( vec{v} ) is given by ( frac{vec{v}}{||vec{v}||} ). So, the unit vector in the same direction as ( vec{v} ) is ( frac{3hat{i} - 4hat{j} + 2hat{k}}{sqrt{29}} = frac{3}{sqrt{29}}hat{i} - frac{4}{sqrt{29}}hat{j} + frac{2}{sqrt{29}}hat{k} ).

Find a unit vector in the same direction as the given vector $\vec{v} = 3 \hat{i} - 4 \hat{j} + 2 \hat{k}$ .

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Popular Problems

Find a unit vector in the same direction as the given vector v→=3i^−4j^+2k^.

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Find a unit vector in the same direction as the given vector $\vec{v} = 3 \hat{i} - 4 \hat{j} + 2 \hat{k}$ .