Question

Find a unit vector parallel to the resultant vector A1=2i+4j−5k, A2=1+2j+3k
a) 3/7i+6/7j−2/7k
b)1/7i+63/7j−4/7
c)2/7i−3/7j−5/7
d)3/5i+6/5j−2/5

Answer 1

Answer on Question #67860 – Math – Analytic Geometry

Question

Find a unit vector parallel to the resultant vector $A1 = 2i + 4j - 5k$, $A2 = 1 + 2j + 3k$

a) $3/7i + 6/7j - 2/7k$

b) $1/7i + 63/7j - 4/7$

c) $2/7i - 3/7j - 5/7$

d) $3/5i + 6/5j - 2/5$

Solution

The resultant vector of $A_1 = 2i + 4j - 5k$ and $A_2 = i + 2j + 3k$ is

$$A = A_1 + A_2 = (2i + 4j - 5k) + (i + 2j + 3k) = (2 + 1)i + (4 + 2)j + (-5 + 3)k = 3i + 6j - 2k.$$

Its length is

$$|A| = \sqrt{9 + 36 + 4} = 7.$$

A unit vector parallel to the resultant vector is

$$\frac{A}{|A|} = \frac{3}{7}i + \frac{6}{7}j - \frac{2}{7}k.$$

Answer: a) $\frac{3}{7}i + \frac{6}{7}j - \frac{2}{7}k.$

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