Question

The unit vector parallel to the resultant of the
vectors Ā = 2i+4j-5k and B = i+2j+3k is​

Answer 1

Here is your answer,

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vector A = 2i+4j-5k

vector B = i+2j+3k

To find the parallel vector for the given two vectors, its sum should be calculated ,

A+B = 2i + i + 4j + 2j  - 5k + 3k

       = 3i + 6j - 2k

$\sqrt{A+B}$ = $\sqrt{(3^{2}) + 6^{2} + (-2)^{2} }$

             = $\sqrt{9+36+4}$

             = $\sqrt{49}$

             = 7

Unit vector = vector AB / \sqrt{A+B}

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

Answer 2

The unit vector parallel to the resultant of the vectors Ā = 2i+4j-5k and B = i+2j+3k is​  ( 3i + 6j - 2k ) / 7

Given:  Ā = 2i + 4j - 5k and B = i + 2j + 3k

To Find: The unit vector parallel to the resultant of the vectors

Ā = 2i + 4j - 5k and B = i + 2j + 3k

Solution:

We know that to find the resultant of two vectors we use the law of addition of two vectors. So, we find the sum of the two vectors,

Let's call the resultant vector , C

C = A+B = 2i + i + 4j + 2j  - 5k + 3k

              = 3i + 6j - 2k

A unit vector parallel to another vector is found using the formula;

P = P / | P |                        [where | P | is the modulus value of the vector]

Now,

| C | = √ (  3² + 6² + 2² )

      =  √49

      =  7

So, writing the unit vector C ,

C = C / | C |

   = ( 3i + 6j - 2k ) / 7

Hence the unit vector parallel to the resultant of the vectors Ā = 2i+4j-5k and B = i+2j+3k is​  ( 3i + 6j - 2k ) / 7

         

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