ContohSoalUAN Vektor

(1)

(2)

(3)

(4)

PEMBAHASAN:

1. Jawab: B

= R – P = – – = – – –

= Q – R = _– – – = _–

cos = =

– – –

–

= – = 0 = 90

2. Jawab: D

2

= 2 + 2 + 2 ( )2 = ( )2 + 2 . + ( )2 5 = 2 + 2 . + 9

5 = 11 + 2 . 2 . = 5 – 11 2 . = – 6 . = – 3

cos = = – = – = – = 180 – 45 = 135

3. Jawab: B

(5)

4. Jawab: B

cos = = = – = – = – 3

2_{= 9} 2_{+ 12} _{+ 4} 2 = 9 ( 2 )2 + 12 ( –3 ) + 4 ( 3 )2 = 36 – 36 + 36

= 36 = 6

5. Jawab: C

2

= 2– 2 + 2 ( 1 )2 = ( )2– 2 + ( 1 )2 1 = 3 – 2 + 1

=

2

= 2 + 2 + 2 = ( )2 + 2 . + ( 1 )2 = 3 + 3 + 1

=

6. Jawab: C

( –_{)( + ) = 0} 2– 2 = 0 2 = 2 = =

( – ) = 3 2– = 3

= ( )2 – 3 = 6 – 3 = 3

(6)

7. Jawab: A

= – = – =

Proyeksi Orthogonal:

x = = = =

Sehingga proyeksi orthogonal pada adalah +

8. Jawab: A

a = – –

; b = – ; c = –

( + ) = – –

+ – = –

–

Panjang proyeksi:

= =

–

– –

-= – = = 3

9. Jawab: E

x = =

–

– –

– – =

–

– = –

(7)

Sehingga proyeksi orthogonal pada adalah – + – 2

10. Jawab: D

x = =

– –

–

– –

–

= – – –

–

= –

11. Jawab: A

Panjang proyeksi:

= = –

–

= – = =

=

x = = 2

Sehinnga cos :

cos = = – = – = =

12. Jawab: C

a = – ; b =

Panjang proyeksi:

= =

–

(8)

=

2p = ( kedua ruas dikuadratkan ) 4p2 = 12 + p2

3p2 = 12 p2 = 4

p = 2 ( p = 2 atau p = –2 )

13. Jawab: A

: = ( – ) : ( – )

= – : –

= :

= 1 : 2

14. Jawab:

AP : PB = 1 : 3 P =

P = – –

– – ₌

–

= – = – – –

–

– =

– –

(9)

15. Jawab:

16. Jawab: E

AB : BC ( – ) : ( – )

_– –

– : _–– – –

–_– : – AB : BC = 1 : 3

Sehingga: p + 1 = –12 p = – 13

***

Titik berat =

= –

–