Diketahui vektor a =
[tex] \binom{4}{ - 6} [/tex] dan b =
[tex] \binom{ - 3}{p} [/tex]Jika vektor a tegak lurus b, nilai p adalah
[tex] \binom{4}{ - 6} [/tex] dan b =
[tex] \binom{ - 3}{p} [/tex]Jika vektor a tegak lurus b, nilai p adalah
Jawab:
–2
Penjelasan dengan langkah-langkah:
Vektor Saling Tegak Lurus
[tex]\large\text{$\begin{aligned}&\overrightarrow{a}=\begin{pmatrix}4\\-6\end{pmatrix}\ ,\ \ \overrightarrow{b}\begin{pmatrix}-3\\p\end{pmatrix}\ ,\ \ \overrightarrow{a}\perp\overrightarrow{b}\end{aligned}$}[/tex]
[tex]\large\text{$\begin{aligned}&\textsf{Karena kedua vektor saling tegak lurus, maka:}\\&\overrightarrow{a}\cdot\overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|\cos90^\circ\\&{\iff}\overrightarrow{a}\cdot\overrightarrow{b}=0\\&{\iff}\begin{pmatrix}4\\-6\end{pmatrix}\cdot\begin{pmatrix}-3\\p\end{pmatrix}=0\\&{\iff}4(-3)+(-6p)=0\\&{\iff}-12=6p\\&{\iff}p=\bf-2\end{aligned}$}[/tex]
