# Bab 15 Vektor

4.6 Vektor, SPM Praktis (Kertas 1)
Soalan 5:
Gunakan maklumat di atas untuk mencari nilai h dan nilai k apabila r= 2p – 3q.

Penyelesaian:
$\begin{array}{l}r=2p-3q\\ \left(h-1\right)\underset{˜}{a}+\left(h+k\right)\underset{˜}{b}=2\left(5\underset{˜}{a}-7\underset{˜}{b}\right)-3\left(-2\underset{˜}{a}+3\underset{˜}{b}\right)\\ \left(h-1\right)\underset{˜}{a}+\left(h+k\right)\underset{˜}{b}=10\underset{˜}{a}-14\underset{˜}{b}+6\underset{˜}{a}-9\underset{˜}{b}\\ \left(h-1\right)\underset{˜}{a}+\left(h+k\right)\underset{˜}{b}=16\underset{˜}{a}-23\underset{˜}{b}\end{array}$

Bandingkan vektor,
h– 1 = 16
h = 17
h+ k = –23
17 + k = –23
k = –40

Soalan 6:
Titik-titik P, Qdan R adalah segaris. Diberi bahawa , dengan keadaan kialah pemalar. Cari
(a)  nilai k,
(b)  nisbah PQ : QR.

Penyelesaian:
(a)

(b)
$\begin{array}{l}\stackrel{\to }{PQ}=m\stackrel{\to }{QR}\\ \stackrel{\to }{PQ}=\frac{4}{3}\stackrel{\to }{QR}\\ \frac{\stackrel{\to }{PQ}}{\stackrel{\to }{QR}}=\frac{4}{3}\\ \therefore PQ:QR=4:3\end{array}$

Soalan 7:
Diberi bahawa , cari nilai m jika vektor

Penyelesaian: