Question

If a=i+2j-3k and b=2i+4j+9k then find unit vector parallel to a+b

Answer 1

3i+6j+6k/(9+36+36)^1/2

3i+6j+6k/9

is the answer

hope this helps you

Answer 2

Unit parallel vector is

$\displaystyle\frac{1}{3}i + \frac{2}{3}j + \frac{2}{3}k$

Step-by-step explanation:

We are given the following in the question:

$a=i+2j-3k\\b=2i+4j+9k$

Sum of vectors =

$a + b = i+2j-3k + (2i+4j+9k)\\a + b = 3i+6j+6k$

Magnitude can be found as:

$|a+b| = \sqrt{3^2 + 6^2 + 6^2} = \sqrt{81} = 9$

Parallel unit vector is given by:

$\dfrac{a+b}{|a+b|}\\\\=\dfrac{3i + 6j + jk}{9}\\\\=\displaystyle\frac{1}{3}i + \frac{2}{3}j + \frac{2}{3}k$

is the required vector.

#LearnMore

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