Question

Find the component of u along v.

u= (-4,6), and v=$(1\sqrt{2}, 1\sqrt{2} )$

Answer 1

u. The distance we travel in the direction of v, while traversing u is called the component of u with respect to v and is denoted compvu. The vector parallel to v, with magnitude compvu, in the direction of v is called the projection of u onto v and is denoted projvu.

Answer 2

Answer:

$comp_vu=\sqrt{2}$

Step-by-step explanation:

The component of vector u along v is $comp_vu=\frac{u\bullet v}{||v||}$ where $u\bullet v$ is the dot product and $||v||$ is the magnitude of vector v.

The dot product is $u\bullet v=u_1v_1+u_2v_2=(-4)(1\sqrt{2})+(6)(1\sqrt{2})=2\sqrt{2}$

The magnitude of vector v is $||v||=\sqrt{v_1^2+v_2^2}=\sqrt{(1\sqrt{2})^2+(1\sqrt{2})^2}=\sqrt{2+2}=\sqrt{4}=2$

Therefore, the component of vector u along v is $comp_vu=\frac{u\bullet v}{||v||}=\frac{2\sqrt{2}}{2}=\sqrt{2}$