Question

How to find a unit vectors along the directions of the vectors 5i-3j+4k?

Answer 1

suppose a = 5i-3j+4k then |a| = √50 then unit vector in that direction of a is 5/√50i - 3/√50j + 4/√50k

Answer 2

Answer:

$\hat{a}=\frac{5i-3j+4k}{5\sqrt{2} }$

Step-by-step explanation:

Given: A vector $5i-3j+4k$.

To find: Unit vector along the direction of given vector.

We know that unit vector along the direction of given vector $\vec{a}$ is given by:

$\hat{a}=\frac{\vec{a}}{|a|}$

Here, $\vec{a}=5i-3j+4k$

And $|\vec{a}|=\sqrt{5^{2}+(-3)^{2}+4^{2} }$

           $=\sqrt{50} \\=5\sqrt{2}$

Hence, unit vector along given vector is: $\hat{a}=\frac{5i-3j+4k}{5\sqrt{2} }$.

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