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musickatia [10]
3 years ago
10

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

Mathematics
1 answer:
Soloha48 [4]3 years ago
7 0

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}

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