Question

Determine the projection of w onto u

Answer 1

Answer:

c. 6.2i - 4.2j

Step-by-step explanation:

The vector projection when the angle θ not known can be calculated  using the following property of the dot product:

$proj_uv=\frac{u\cdot v}{||u||^2} u$

Where the dot product of two vectors is given by:

$u\cdot v= \sum_{i=1}^{n} u_iv_i= u_1v_1+u_2v_2+...+u_nv_n$

And the magnitude of a vector is given by:

$||u||=\sqrt{u_1^2+u_2^2+...+u_n^2}$

Using the previous definition, let's calculate the projection of w onto u:

First let's calculate the dot product between w and u:

$u\cdot w =(9*19)+(-6*15)=171-90=81$

Now let's find the magnitude of u:

$||u||=\sqrt{9^2+(-6)^2} = 3 \sqrt{13}$

So:

$||u||^2=117$

Therefore:

$proj_uw=\frac{u\cdot w}{||u||^2} u=\frac{81}{117} \langle9,-6\rangle=\langle6.23,-4.14\rangle\approx6.2i-4.2j$

Answer 2

Answer:

c. 6.2i - 4.2j