Diketahui sebuah vektor u = ( a,-2-1 ) dan v ( a,a,-1 ) jika vektor u tegak lurus pada v maka tentukanlah a. 3u - 5v

Vektor yg saling tegak lurus, maka hasil perkalian nya = 0
u'v = 0
a×a + (-2)×a + (-1)×(-1) = 0
a²- 2a + 1 = 0
(a-1)² = 0
a-1 = 0
a = 1

Jadi, a = 1

u = ( a,-2-1 ) = ( 1, -2, -1)
v = ( a,a,-1 ) = ( 1, 1, -1 )

3u - 5v = 3 × ( 1, -2, -1) - 5 × ( 1, 1, -1 )
3u - 5v = ( 3, -6, -3 ) - ( 5, 5, -5 )
3u - 5v = ( 3-5, -6-5, -3-(-5) )
3u - 5v = ( -2, -11, -3+5)
3u - 5v = ( -2, -11, 2 )

Jadi, 3u - 5v = ( -2, -11, 2 )