Question

Find the unit vector parallel to the resultant of the vectors a=2i-6j-3k and b=4i+3j-k

Answer 1

Answer:

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Answer 2

Answer:

The unit vector parallel to the resultant of the vectors $A=2i-6j-3k$ and $B=4i+3j-k$ is

$n=\frac{6i-3j-4k}{\sqrt{61} }$

Explanation:

The unit vector of any vector A is given by the formula,

$n=\frac{A}{/A/}$

where $/A/$ is the magnitude of the vector A

from the question, we are asked to find out the unit vector parallel to two vectors, that are

$A=2i-6j-3k$ and $B=4i+3j-k$

the resultant of these vectors $A+B= (2+4)i+(-6+3)j+(-3+-1)k=6i-3j-4k$

now the magnitude of the resultant vector $/R/=\sqrt{6^{2} +3^{2} +4^{2} } =\sqrt{61}$

unit vector along the resultant vector is

$n=\frac{A+B}{/A+B/}$

$n=\frac{6i-3j-4k}{\sqrt{61} }$