Question

A vector equals to 4 icap + 4 j cap - 4 k cap and b vector equals to b icap + 2 j cap + 4 k cap then angle between a vector and b vector is

Answer 1

Answer:

vector

4 icap 4j cap 4k cap and b

ica0 2 j cap

4k cap

Answer 2

Answer:

The angle between the vectors $A=4i+4j-4k$ and $B=i+2j+4k$ is 82.5⁰

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 angle between two vectors $A=ai+bj+ck$ and $B=di+ej+fk$ is

        Ф=$cos^{-1} (\frac{A.B}{/A//B/})$

        where $A.B$ is the dot product

From the question, we have

the component form of the vector $A=4i+4j-4k$

the component form of the vector $B=i+2j+4k$

the magnitude of the vector $/A/=\sqrt{4^{2} +4^{2}+4^{2} } =6.8$ unit

the magnitude of the vector $/A/=\sqrt{1^{2} +2^{2}+4^{2} } =4.58$ unit

the dot product of the vectors $A.B=(4*1)+(4*2)+(-4*4)=4+8-16=-4$

therefore the angle is $cos^{-1} (\frac{-4}{6.8*4.5} )=cos^{-1}(0.13)=82.5$