Question

A unit vector of a vector a vector equal to two icap + 3 j cap + 4 k cap is

Answer 1

Answer:

unit vector means magnitude

Explanation:

$\sqrt{29}$

Answer 2

Answer:

The unit vector in the direction of vector A=2i + 3j +4k is $A//A/=\frac{2i+3j+4k}{\sqrt{29} }$

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 $A=2i+3j+4k$

as compared to the above equation

$a=2 \\b=3\\c=4$

now the magnitude of the vector $/A/=\sqrt{3^{2} +2^{2}+4^{2} } =\sqrt{29}$ unit

the unit vector along the given vector is $A//A/=\frac{2i+3j+4k}{\sqrt{29} }$