Diketahui proyeksi scalar ortogonal a= ( 8 -2 4) pada b= ( m 0 4) adalah 8 , panjang a+ 2b adalah

diketahui
a = (8, -2, 4)
b = (m, 0, 4)

a.b = (x1.x2) + (y1.y2) + (z1.z2)
a.b = (8.m) + (-2.0) + (4.4)
a.b = 8m + 16

|b| = √x2² + y2² + z2²
|b| = √m² + 16

proyeksi scalar = a.b/|b|
8 = 8m + 16/|b|
8|b| = 8m + 16
|b| = 8m + 16/8
|b| = m + 2

√m² +16 = m + 2
m² + 16 = (m + 2)²
m² + 16 = m² + 4m + 4
m² - m² = 4m + 4 - 16
0 = 4m -12
12 = 4m
m = 3

a = (8, -2, 4)
2b = 2(3, 0, 4)
2b = (6, 0, 8)
a + 2b = (8, -2, 4) + (6, 0, 8)
a + 2b = (14, -2, 12)
|a + 2b| = √14² + (-2)² + 12²
|a + 2b| = √196 + 4 + 144
|a + 2b| = √344
|a + 2b| = 2√86

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