Question

What is the correct expression of position vector rcb (in feet)?

Answer 1

Answer:

4i+j-2k

Step-by-step explanation:

The missing figure in this problem as been attached, as we can see the figure is a 3-D figure consisting of rods with point C and B.

Using the figure we can find the value of position vector $r_{cb}$

r$_{CB}$=$r_{b}$-$r_{c}$

As we know , a position vector is the difference of position vector of ending point to the position vector of starting point, here the starting point is C and ending point is B. Hence, the expression above.

We need to first find $r_{b}$ and $r_{c}$

Using the figure:

$r_{b}$ =0i+4j+2k

$r_{c}$ = -4i+3j+4k

r$_{CB}$=$r_{b}$-$r_{c}$=(0i+4j+2k) - (-4i+3j+4k)

r$_{CB}$=4i+j-2k (feet)

Magnitude of $r_{cb}$=$\sqrt{4^{2}+(1)^{2}-2^{2} }$=$\sqrt{21}$=4.583 ft