Question

if vector A = 3i-4j and B=2i+16j then the magnitude and direction of vector A+B will be ​

Answer 1

Step-by-step explanation:

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Answer 2

The magnitude and direction of vector A+B is 13 and  $tan^{-1}\frac{12}{5}$.

Given:

A = 3i -4j and B =2i+16j

To Find:

The magnitude and direction of the vector A+B.

Solution:

We have to add the coefficient of I and the coefficient of j of A and B.

A+B = (3+2)i + (-4+16)j

=5i+12j

Magnitude | A+B|

$=\sqrt{5^{2}+12^{2} } \\\\= \sqrt{25+144} \\\\\\=\sqrt{169} \\\\=13$

The direction of A+B (θ)

$=tan^{-1} \frac{Coefficient \ of \ j}{Coefficient \ of \ i} \\\\=tan^{-1}\frac{12}{5}$

Therefore, the magnitude and direction of vector A+B is 13 and  $tan^{-1}\frac{12}{5}$.

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