Soal vektor, mohon dibantu kak T_T

Soal vektor, mohon dibantu kak T_T

vektor

P = 2i + 3j + 4k

Q = i – 5j + 2k

P • Q

= (2,3,4) • (1,-5,2)

= (2 . 1) + (3 . (-5)) + (4 . 2)

= 2 – 15 + 8

= -5

P × Q

= i(3.2 – 4(-5)) – j(2.2 – 1.4) + k(2(-5) – 1.3)

= 26i – 0j – 13k

= 26i – 13k

$vec{text{P}}:=:2vec{i}:+:3vec{j}:+:4vec{k}$

$vec{text{Q}}:=:vec{i}-5vec{j}+2vec{k}$

Dot product (perkalian titik) :

$vec{text{P}}.vec{text{Q}}:=:(2).(1):+:(3).(-5):+:(4).(2)$

$vec{text{P}}.vec{text{Q}}:=:2:-15:+:8$

$boxed{boxed{vec{text{P}}.vec{text{Q}}:=:-5}}$

Cross product (perkalian silang) :

Perlu diketahui :

Jika didefinisikan :

$vec{text{A}}:=:A_ivec{i}:+:A_jvec{j}:+:A_kvec{k}$

$vec{text{B}}:=:B_ivec{i}:+:B_jvec{j}:+:B_kvec{k}$

Maka, A × B (dibaca : perkalian silang/cross product vektor A & vektor B) adalah :

$vec{text{A}}:times:vec{text{B}}:=:(A_j.B_k:-:A_k.B_j)vec{i}:+:(A_k.B_i:-:A_i.B_k)vec{j}:+:(A_i.B_j:-:A_j.B_i)vec{k}$

Sehingga :

$vec{text{P}}:times:vec{text{Q}}:=:([3].[2]:-:[4].[-5])vec{i}:+:([4].[1]:-:[2].[2])vec{j}:+:([2].[-5]:-:[3].[1])vec{k}$

$vec{text{P}}:times:vec{text{Q}}:=:(6:+:20)vec{i}:+:(4:-:4)vec{j}:+:(-10:-:3)vec{k}$

$boxed{boxed{vec{text{P}}:times:vec{text{Q}}:=:26vec{i}:-:13vec{k}}}$