Q:

how do I find the value of k​

Accepted Solution

A:
The value of k is 2/5[tex]\texttt{ }[/tex]Further explanationVector is quantity that has magnitude and direction.One example of a vector is acceleration.Let us now tackle the problem ![tex]\texttt{ }[/tex]This problem is about Vector Diagram.[tex]\overrightarrow{OA} = \overrightarrow{a}[/tex][tex]\overrightarrow{OC} = \overrightarrow{c}[/tex]X is the midpoint of the line AC:[tex]\overrightarrow{x} = \frac{1}{2} (\overrightarrow{a} + \overrightarrow{c})[/tex][tex]\texttt{ }[/tex]OC : CD = k : 1[tex]k \overrightarrow{CD} = \overrightarrow{OC}}[/tex][tex]k( \overrightarrow{d} - \overrightarrow{c} ) = \overrightarrow{c}}[/tex][tex]( \overrightarrow{d} - \overrightarrow{c} ) = \frac{1}{k} \overrightarrow{c}}[/tex][tex]\overrightarrow{d} = \overrightarrow{c} + \frac{1}{k} \overrightarrow{c}}[/tex][tex]\overrightarrow{d} = ( 1 + \frac{1}{k} ) \overrightarrow{c}}[/tex][tex]\texttt{ }[/tex][tex]\overrightarrow{XD} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex][tex]\overrightarrow{d} - \overrightarrow{x} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex][tex]( 1 + \frac{1}{k} ) \overrightarrow{c} - \frac{1}{2} (\overrightarrow{a} + \overrightarrow{c}) = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex][tex]( 1 + \frac{1}{k} - \frac{1}{2}) \overrightarrow{c} - \frac{1}{2} \overrightarrow{a} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex][tex]( \frac{1}{k} + \frac{1}{2}) \overrightarrow{c} - \frac{1}{2} \overrightarrow{a} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}[/tex][tex]\frac{1}{k} + \frac{1}{2} = 3[/tex][tex]\frac{1}{k} = 3 - \frac{1}{2}[/tex][tex]\frac{1}{k} = \frac{5}{2}[/tex][tex]k = \frac{2}{5}[/tex][tex]\texttt{ }[/tex]Learn moreVelocity of Runner : Energy : : Speed of Car : detailsGrade: High SchoolSubject: MathematicsChapter: VectorsKeywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate, Stream , Vector