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Anvisha [2.4K]
2 years ago
14

Find a vector of magnitude 3 in the direction of v = 10i - 24k. The vector is Oi-Oj+k (Simplify your answer. Use integers or fra

ctions for any numbers in the expression).
Mathematics
1 answer:
Soloha48 [4]2 years ago
6 0

Given :

A vector v = 10i - 24k.

To Find :

A vector of magnitude 3 in the direction of v = 10i - 24k.

Solution :

Unit vector in the direction  of vector v is :

\^{v}=\dfrac{v}{|v|}\\\\\^{v}=\dfrac{10i-24k}{\sqrt{10^2+24^2}}\\\\\^{v}=\dfrac{10i-24k}{26}

Now , vector of magnitude 3 in direction v is :

r=3 \^{v}\\\\r=3\times \dfrac{ (10i-24k)}{26}\\\\r=\dfrac{3}{13} (5i-12k)

Hence , this is the required solution .

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