2 Answers

Jacman · Answer 1 · 2021-12-31T12:54:09+0000

Answer:

$8\hat i-2\hat j-2\hat k$

Step-by-step explanation:

Vectors in 3D

Given a vector

$\vec P = P_x\hat i+P_y\hat j+P_z\hat k$

A vector
$\vec Q$ parallel to
$\vec P$ is:

$\vec Q = k.\vec P$

Where k is any constant different from zero.

We are given the vectors:

$\vec A = \hat i+4\hat j-2\hat k$

$\vec B = 3\hat i-5\hat j+\hat k$

It's not specified what the 'resultant' is about, we'll assume it's the result of the sum of both vectors, thus:

$\vec A +\vec B = \hat i+4\hat j-2\hat k + 3\hat i-5\hat j+\hat k$

Adding each component separately:

$\vec A +\vec B = 4\hat i-\hat j-\hat k$

To find a vector parallel to the sum, we select k=2:

$2(\vec A +\vec B )= 8\hat i-2\hat j-2\hat k$

Thus one vector parallel to the resultant of both vectors is:

$\mathbf{8\hat i-2\hat j-2\hat k}$

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