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Magazine Problem 33
Express the given vector (a) in trigonometric form and (b) as a linear combination of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$ \langle-\sqrt{2}, \sqrt{2}\rangle $$
Problem 34
Express the given vector (a) in trigonometric form and (b) as a linear combination of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$ \langle 7,7 \sqrt{3}\rangle $$
Problem 35
Express the given vector (a) in trigonometric form and (b) as a linear combination of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$ \langle-3 \sqrt{3}, 3\rangle $$
Problem 36
Express the given vector (a) in trigonometric form and (b) as a linear combination of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$ \langle-4,-4\rangle $$
Problem 37
Find a unit vector (a) in the same direction as \(\mathbf{v}\), and \(\mathbf{( b )}\) in the opposite direction of \(\mathbf{v}\). $$ \mathbf{v}=\langle 2,2\rangle $$
Problem 38
Find a unit vector (a) in the same direction as \(\mathbf{v}\), and \(\mathbf{( b )}\) in the opposite direction of \(\mathbf{v}\). $$ \mathbf{v}=\langle-3,4\rangle $$
Problem 39
Find a unit vector (a) in the same direction as \(\mathbf{v}\), and \(\mathbf{( b )}\) in the opposite direction of \(\mathbf{v}\). $$ \mathbf{v}=\langle-3,4\rangle $$
Problem 40
Find a unit vector (a) in the same direction as \(\mathbf{v}\), and \(\mathbf{( b )}\) in the opposite direction of \(\mathbf{v}\). $$ \mathbf{v}=\langle 1,-\sqrt{3}\rangle $$
Problem 41
Normalize the given vector when \(\mathbf{v}=\langle 2,8\rangle\) and \(\mathbf{w}=\langle 3,4\rangle\). $$ \mathbf{V}+\mathbf{W} $$
Problem 42
Normalize the given vector when \(\mathbf{v}=\langle 2,8\rangle\) and \(\mathbf{w}=\langle 3,4\rangle\). $$ 2 \mathbf{v}-3 \mathbf{W} $$
