Question

Given the displacement vector A=3i-4j+4k,B=2i+3j-7k. Find the magnitude of the vector a) A+B and b)2A-B

Answer 1

Answer:

The magnitudes of the vectors $\vec A +\vec B$ and $2\vec A -\vec B$ are $\sqrt{35}$ and $\sqrt{602}$ respectively.

Step-by-Step Explanation:

Consider the displacement vectors as follows:

$\vec A=3i-4j+4k$ and $\vec B=2i+3j-7k$

Compute $\vec A +\vec B$ as follows:

$\vec A +\vec B=(3i-4j+4k)+(2i+3j-7k)$

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

Then, the magnitude of the vector $\vec A +\vec B$ is as follows:

$|\vec A +\vec B|=|5j-j-3k|$

$|\vec A +\vec B|=\sqrt{5^2+(-1)^2+(-3)^2}$

            $=\sqrt{25+1+9}$

            $=\sqrt{35}$

Thus, the magnitude of the vector $\vec A +\vec B$ is $\sqrt{35}$.

Similarly,

Compute $2\vec A -\vec B$ as follows:

$2\vec A -\vec B=2(3i-4j+4k)-(2i+3j-7k)$

$2\vec A -\vec B=6i-8j+8k-2i-3j+7k$

$2\vec A -\vec B=4i-11j+15k$

Then, the magnitude of the vector $2\vec A -\vec B$ is as follows:

$|2\vec A -\vec B|=|4j-11j+15k|$

$|\vec A +\vec B|=\sqrt{16^2+(-11)^2+15^2}$

            $=\sqrt{256+121+225}$

            $=\sqrt{602}$

Therefore, the magnitude of the vector $2\vec A -\vec B$ is $\sqrt{602}$.

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