Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 55
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ \mathbf{u} \cdot(4 \mathbf{v}) $$
Problem 56
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ \mathbf{v} \cdot(\mathbf{u}-\mathbf{w}) $$
Problem 57
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ (-\mathbf{v}) \cdot\left(\frac{1}{2} \mathbf{w}\right) $$
Problem 58
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ (2 \mathbf{v}) \cdot(3 \mathbf{w}) $$
Problem 59
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ \mathbf{u} \cdot(\mathbf{u}+\mathbf{v}+\mathbf{w}) $$
Problem 60
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ (2 \mathbf{u}) \cdot(\mathbf{u}-2 \mathbf{v}) $$
Problem 61
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ \left(\frac{\mathbf{u} \cdot \mathbf{v}}{\mathbf{v} \cdot \mathbf{v}}\right) \mathbf{v} $$
Problem 62
In Problems \(49-62, \mathbf{u}=\langle 2,-3\rangle, \mathbf{v}=\langle-1,5\rangle,\) and \(\mathbf{w}=\langle 3,-2\rangle .\) Find the indicated scalar or vector. $$ (\mathbf{w} \cdot \mathbf{v}) \mathbf{u} $$
Problem 63
Find the dot product \(\mathbf{u} \cdot \mathbf{v}\) if the smaller angle between \(\mathbf{u}\) and \(\mathbf{v}\) is as given. $$ |\mathbf{u}|=10,|\mathbf{v}|=5, \theta=\pi / 4 $$
Problem 64
Find the dot product \(\mathbf{u} \cdot \mathbf{v}\) if the smaller angle between \(\mathbf{u}\) and \(\mathbf{v}\) is as given. $$ |\mathbf{u}|=6,|\mathbf{v}|=12, \theta=\pi / 6 $$
