Question

yang bisa dan mengerti, tolong bantuannya ya
beserta jawabannya

ini matkul Fisika Mekanika​

Answer 1

[tex]\bf »\;\; \vec A = 3\hat i+2\hat j+\hat k \;\text{ dan }\; \vec B = 2\hat i-\hat j+\hat k [/tex]

Hasil perkalian titik (dot product) :

[tex] \begin{aligned} \vec A \boldsymbol{\cdot} \vec B &= 3\cdot 2+2\cdot (-1)+1\cdot 1 \\ &= 6-2+1 \\ &= 5\end{aligned} [/tex]

Hasil perkalian silang (cross product) :

[tex]\begin{aligned} \vec A \times \vec B &= \begin{array}{|ccc|cc} \hat i&\hat j & \hat k& \hat i&\hat j \\ 3&2&1&3&2 \\ 2&-1&1&2&-1 \\ \end{array} \\ &=( 2\hat i+2\hat j-3\hat k)-(4\hat k-\hat i+3\hat j) \\ &= 2\hat i+2\hat j-3\hat k-4\hat k+\hat i-3\hat j \\ &= 3\hat i-\hat j-7\hat k \end{aligned} [/tex]

[tex]\rm »\;\; \vec A = \hat i-3\hat j+4\hat k \;\text{ dan }\; \vec B = -\hat i-2\hat j+2\hat k [/tex]

Hasil perkalian titik (dot product) :

[tex] \begin{aligned} \rm \vec A \boldsymbol{\cdot} \vec B &= 1\cdot (-1)+(-3)\cdot (-2)+4\cdot 2 \\ &= -1+6+8 \\ &= 13 \end{aligned} [/tex]

Hasil perkalian silang (cross product) :

[tex]\begin{aligned} \rm \vec A \times \vec B &= \rm \begin{array}{|ccc|cc} \hat i&\hat j & \hat k& \hat i&\hat j \\ 1&-3&4&1&-3 \\ -1&-2&2&-1&-2 \\ \end{array} \\ &=( -6\hat i-4\hat j-2\hat k)-(3\hat k-4\hat i+2\hat j) \\ &= -6\hat i-4\hat j-2\hat k-3\hat k+4\hat i-2\hat j \\ &= -2\hat i-6\hat j-5\hat k \end{aligned} [/tex]