Question

Misalkan u = (2,0, −3), v = (0, −4,2) dan w= (−2,1, −1). Maka (2u − 4w ) ∙ v adalah ...
A. 10
B. 12
C. 15
D. 14

Answer 1

(2u − 4w ) · v = 12
 

Pembahasan

Vektor

Diketahui

Vektor-vektor:

• u = (2, 0, −3),
• v = (0, –4, 2), dan
• w = (−2, 1, −1)

Ditanyakan

• (2u − 4w ) · v

PENYELESAIAN

(2u − 4w ) · v

= ( 2(2, 0, −3) – 4(−2, 1, −1) ) · (0, –4, 2)

= (4+8, 0–4, –6+4) · (0, –4, 2)

= (12, –4, –2) · (0, –4, 2)

= 12·0 + (–4)(–4) + (–2)·2

= 0 + 16 + (–4)

= 12
 

KESIMPULAN

∴  (2u − 4w ) · v = 12