Free Printable Vektor

1.

jika vektor $\overrightarrow{a}=\left(1,2,3\right),\ \overrightarrow{b}=\left(5,4,-1\right)\ dan\ \overrightarrow{c}=\left(4,-1,1\right),$ maka vektor $\overrightarrow{a}+2\overrightarrow{b}-3\overrightarrow{c}=...$

a)

$6\overrightarrow{i}+11\overrightarrow{j}-8\overrightarrow{k}$

b)

$7\overrightarrow{i}+13\overrightarrow{j}-8\overrightarrow{k}$

c)

$-\overrightarrow{i}+12\overrightarrow{j}-2\overrightarrow{k}$

d)

$-\overrightarrow{i}+13\overrightarrow{j}-2\overrightarrow{k}$

e)

$-6\overrightarrow{i}-12\overrightarrow{j}+8\overrightarrow{k}$

2.

Diketahui $\left|\overrightarrow{a}\right|=\sqrt{3},\ \left|\overrightarrow{b}\right|=1,\ dan\ \left|\overrightarrow{a}-\overrightarrow{b}\right|=1.$ panjang vektor $\overrightarrow{a}+\overrightarrow{b}\ =...$

a)

$\sqrt{3}$

b)

$\sqrt{5}$

c)

$\sqrt{7}$

d)

$2\sqrt{2}$

e)

3

3.

Titik $A\ \left(4,7,0\right),\ B\left(6,10,-6\right),\ C\left(1,9,0\right),\ \overrightarrow{AB}=\overrightarrow{u}\ dan\ \overrightarrow{AC}=\overrightarrow{v},$ Sudut $BAC$ adalah sudut yang dibentuk oleh vektor $\overrightarrow{u}\ dan\ \overrightarrow{v,}$ maka besar sudut $BAC=...$

a)

$\frac{1}{3}\pi$

b)

$\frac{1}{4}\pi$

c)

$\frac{2}{3}\pi$

d)

$\frac{5}{6}\pi$

e)

$\frac{1}{2}\pi$

4.

Jika nilai $\left|\overrightarrow{a}\right|=8,\ \left|\overrightarrow{b}\right|=4,\ \angle\left(\overrightarrow{a},\overrightarrow{b}\right)=60^o$ maka nilai $\left|\overrightarrow{a}-\overrightarrow{b}\right|=\ ....$

a)

3

b)

6

c)

10

d)

$4\sqrt{2}$

e)

$4\sqrt{3}$

5.

Diketahui segitiga ABC, P membagi AB dengan AP : PB = 2 : 1 dan Q titik tengah AC. Jika $\overrightarrow{CA}=\overrightarrow{u}$ dan $\overrightarrow{CB}=\overrightarrow{v}$ , maka $\overrightarrow{PQ}$ = ....

a)

$\frac{1}{3}\overrightarrow{v}-\overrightarrow{u}$

b)

$\overrightarrow{v}-\frac{1}{3}\overrightarrow{u}$

c)

$\frac{1}{3}\overrightarrow{v}-\frac{1}{6}\overrightarrow{u}$

d)

$\frac{1}{6}\overrightarrow{u}-\frac{2}{3}\overrightarrow{v}$

e)

$\frac{1}{6}\overrightarrow{u}+\frac{1}{3}\overrightarrow{v}$

6.

Diketahui $\overrightarrow{a}=4i-5j+3k$ , $\overrightarrow{b}=2i+2j+k$ , dan $\overrightarrow{c}=4i+j-k$ . Jika $\overrightarrow{p}=\overrightarrow{a}-2\overrightarrow{b}+3\overrightarrow{c}$ panjang vektor $\overrightarrow{p}$ adalah ....

a)

$3\sqrt{46}$

b)

$2\sqrt{46}$

c)

$\sqrt{46}$

d)

$\sqrt{23}$

e)

$2\sqrt{23}$

7.

Diketahui A(3, 2, -1) , B(1, -2, 1) dan C(7, p-1, -5) segaris untuk nilai p = ....

a)

13

b)

11

c)

5

d)

-11

e)

-13

8.

Diketahui $u⃗=2i+j-2k\ dan$
$v⃗=i+3j+k.$ Tentukan panjang proyeksi othogonal
$\ u⃗\ pada\ v⃗.$

a)

$1/√11$

b)

$2/√11$

c)

$3/√11$

d)

$4/√11$

e)

$5/√11$

9.

Diketahui vektor satuan $\overrightarrow{u}=0,8\overrightarrow{i}+a\overrightarrow{j},$ jika vektor $\overrightarrow{v}=b\overrightarrow{i}+\overrightarrow{j}$ tegak lurus $\overrightarrow{u}$ , maka $ab=...$

a)

$-\frac{11}{20}$

b)

$-\frac{15}{20}$

c)

$-\frac{12}{20}$

d)

$-\frac{9}{20}$

e)

$-\frac{8}{20}$

10.

Diketahui segitiga $ABC$ dengan $A\left(2,1,2\right),\ B\left(4,-1,3\right),\ dan\ C\left(2,4,11\right).\$ Titik D pada pertengahan BC dan E pada AB sehinggan DE tegak lurus AB, maka panjang AE sama dengan...

a)

1 satuan

b)

2 satuan

c)

3 satuan

d)

4 satuan

e)

5 satuan

Vektor

Total questions: 10

Worksheet time: 39mins

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