Question

Find the unit vector in the direction of vector a is equal to 3 icap + 2 j cap - 5 k cap

Answer 1

Answer:

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Answer 2

Answer:

The unit vector in the direction of vector A=3i + 2j - 5k is $A//A/=\frac{3i+2j-5k}{\sqrt{38} }$

Explanation:

• A vector is a physical quantity described by both magnitude and direction

• The component form of a vector is given by the formula

        $A=ai+bj+ck$

        where $a,b,c$ are components along X, Y, Z axes

        $i,j,k$ are unit vectors along X, Y, Z axes

• The magnitude of that vector can be calculated as $/A/=\sqrt{a^{2} +b^{2}+c^{2} }$

• The unit vector in the direction of the vector is $n=\frac{ai+bj+ck}{\sqrt{a^{2} +b^{2}+c^{2} }}$

From the question, we have

the component force of the vector $A=3i+2j-5k$

as compared to the above equation

$a=3 \\b=2\\c=-5$

now the magnitude of the vector $/A/=\sqrt{3^{2} +2^{2}+5^{2} } =\sqrt{38}$ unit

the unit vector along the given vector is $A//A/=\frac{3i+2j-5k}{\sqrt{38} }$