Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 6
In Exercises \(1-8,\) let \(\mathbf{u}=\langle 3,-2\rangle\) and \(\mathbf{v}=\langle- 2,5\rangle .\) Find the (a) component form and \((\mathbf{b})\) magnitude (length) of the vector. $$ -2 \mathbf{u}+5 \mathbf{v} $$
Problem 6
In Exercises \(1-12,\) give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$ x^{2}+y^{2}=4, \quad z=-2 $$
Problem 6
In Exercises \(1-8,\) find a. \(\mathbf{v} \cdot \mathbf{u},|\mathbf{v}|,|\mathbf{u}|\) b. the cosine of the angle between \(\mathbf{v}\) and \(\mathbf{u}\) c. the scalar component of \(\mathbf{u}\) in the direction of \(\mathbf{v}\) d. the vector projv \(\mathbf{u}\) . $$ \mathbf{v}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{u}=\sqrt{2} \mathbf{i}+\sqrt{3} \mathbf{j}+2 \mathbf{k} $$
Problem 7
In Exercises \(1-8,\) let \(\mathbf{u}=\langle 3,-2\rangle\) and \(\mathbf{v}=\langle- 2,5\rangle .\) Find the (a) component form and \((\mathbf{b})\) magnitude (length) of the vector. $$ \frac{3}{5} \mathbf{u}+\frac{4}{5} \mathbf{v} $$
Problem 7
In Exercises \(1-8,\) find the length and direction (when defined) of \(\mathbf{u} \times \mathbf{v}\) and \(\mathbf{v} \times \mathbf{u} .\) $$ \mathbf{u}=-8 \mathbf{i}-2 \mathbf{j}-4 \mathbf{k}, \quad \mathbf{v}=2 \mathbf{i}+2 \mathbf{j}+\mathbf{k} $$
Problem 7
In Exercises \(1-8,\) find a. \(\mathbf{v} \cdot \mathbf{u},|\mathbf{v}|,|\mathbf{u}|\) b. the cosine of the angle between \(\mathbf{v}\) and \(\mathbf{u}\) c. the scalar component of \(\mathbf{u}\) in the direction of \(\mathbf{v}\) d. the vector projv \(\mathbf{u}\) . $$ \mathbf{v}=5 \mathbf{i}+\mathbf{j}, \quad \mathbf{u}=2 \mathbf{i}+\sqrt{17} \mathbf{j} $$
Problem 7
In Exercises \(1-12,\) give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$ x^{2}+z^{2}=4, \quad y=0 $$
Problem 7
Find parametric equations for the lines in Exercises 1鈥�12. The line through \((1,1,1)\) parallel to the \(z\) -axis
Problem 8
In Exercises \(1-8,\) let \(\mathbf{u}=\langle 3,-2\rangle\) and \(\mathbf{v}=\langle- 2,5\rangle .\) Find the (a) component form and \((\mathbf{b})\) magnitude (length) of the vector. $$ -\frac{5}{13} \mathbf{u}+\frac{12}{13} \mathbf{v} $$
Problem 8
In Exercises \(1-12,\) give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$ y^{2}+z^{2}=1, \quad x=0 $$
