Question

Given T(-2,4,7) and M(-3,5,2) find the ordered triple that represents TM Then find the magnitude of TM-

Answer 1

Answer:

(D)

$\overrightarrow{TM} = < 1, -1, 5 >\\|TM|= 3\sqrt{3}$

Step-by-step explanation:

Given T(-2,4,7) and M(-3,5,2)

$\overrightarrow{TM} = \underline{m} - \underline{t}$  where m and t are position vectors.  $= - < -3, 5, 2> (Subtract corresponding components ) \\= < -2+3, 4- 5, 7-2 >\\= < 1, -1, 5 >$

Given v=<x,y,z>, then the magnitude of v is:

$|v| = \sqrt{x^2+y^2+z^2}, thus \\|TM| = \sqrt{(1)^2+(-1)^2+(5)^2}\\= \sqrt{1+1+25}\\ = \sqrt{27} \\= \sqrt{9*3} \\|TM|= 3\sqrt{3}$