tentukan proyeksi skalar a pada b jika diketahui : a.) a= i - 2j + 3k dan b= -2i + 1j -2k b.) a = 6i + 2j - k dan b= 3i-4j+5k c.) a = 2i + 4j dan b = -8j + 6j +

Proyeksi skalar a pada b = (a.b)/|b|

a) a = i - 2j + 3k
b = -2i + j - 2k => |b| = √((-2)^2 + 1^2 + (-2)^2) = √(4 + 1 + 4) = √9 = 3
=> (a.b)/|b| = (1(-2) + (-2)(1) + 3(-2))/3 = (-2 - 2 - 6)/3 = -10/3

b) a = 6i + 2j - k
b = 3i - 4j + 5k => |b| = √(3^2 + (-4)^2 + 5^2) = √(9 + 16 + 25) = √50 = 5√2
=> (a.b)/|b| = (6(3) + 2(-4) + (-1)(5))/(5√2) = (18 - 8 - 5)/(5√2)
= 5/(5√2) . √2/√2 = (1/2)√2

c) a = 2i + 4j
b = -8i + 6j + 10k => |b| = √((-8)^2 + 6^2 + 10^2) = √(64 + 36 + 100) = √200 = 10√2
=> (a.b)/|b| = (2(-8) + 4(6) + 0(10))/(10√2) = (-16 + 24)/(10√2) = 8/(10√2)
= 4/(5√2) . √2/√2 = (4/10)√2 = (2/5)√2