Free Printable Vektor Mix (28/01/21)

1.

a)

$\sqrt{33}dan\ \left(\frac{1}{\sqrt{33}},\frac{6}{\sqrt{33}}\right)$

b)

$\sqrt{35}dan\ \left(\frac{1}{\sqrt{35}},\frac{6}{\sqrt{35}}\right)$

c)

$\sqrt{37}dan\ \left(\frac{1}{\sqrt{37}},\frac{6}{\sqrt{37}}\right)$

d)

$\sqrt{39}dan\ \left(\frac{1}{\sqrt{39}},\frac{6}{\sqrt{39}}\right)$

2.

a)

$5\ dan\ \left(\frac{4}{5},\frac{-3}{5}\right)$

b)

$6\ dan\ \left(\frac{2}{3},\frac{-1}{2}\right)$

c)

$7\ dan\ \left(\frac{4}{7},\frac{-3}{7}\right)$

d)

$8\ dan\ \left(\frac{1}{2},\frac{3}{8}\right)$

3.

a)

$10\ dan\ \left(\frac{-4}{5},0,\frac{3}{5}\right)$

b)

$10\ dan\ \left(\frac{4}{5},\frac{3}{5}\right)$

c)

$10\ dan\ \left(\frac{4}{5},0,\frac{3}{5}\right)$

d)

$10\ dan\ \left(\frac{4}{5},0,-\frac{3}{5}\right)$

4.

a)

$13\ dan\ \left(\frac{5}{13},\frac{12}{13},0\right)$

b)

$13\ dan\ \left(\frac{-5}{13},\frac{12}{13},0\right)$

c)

$13\ dan\ \left(\frac{5}{13},\frac{-12}{13},0\right)$

d)

$13\ dan\ \left(\frac{-5}{13},\frac{12}{13}\right)$

5.

a)

$\left(7,1\right);\left(6,-6\right);\left(13,5\right)$

b)

$\left(7,1\right);\left(6,-6\right);\left(13,-5\right)$

c)

$\left(-1,1\right);\left(6,-6\right);\left(5,-5\right)$

d)

$\left(-1,1\right);\left(6,-6\right);\left(5,5\right)$

6.

a)

$5\sqrt{3};6\sqrt{2};\sqrt{194}$

b)

$5\sqrt{2};6\sqrt{3};\sqrt{194}$

c)

$5\sqrt{3};6\sqrt{3};\sqrt{194}$

d)

$5\sqrt{2};6\sqrt{2};\sqrt{194}$

7.

a)

$\left(\frac{7}{5\sqrt{2}},\frac{1}{5\sqrt{2}}\right);\left(\frac{6}{6\sqrt{3}},\frac{6}{6\sqrt{3}}\right);\left(\frac{13}{\sqrt{194}},-\frac{5}{\sqrt{194}}\right)$

b)

$\left(\frac{7}{5\sqrt{2}},\frac{1}{5\sqrt{2}}\right);\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right);\left(\frac{13}{\sqrt{194}},-\frac{5}{\sqrt{194}}\right)$

c)

$\left(\frac{7}{5\sqrt{2}},\frac{1}{5\sqrt{2}}\right);\left(\frac{6}{6\sqrt{3}},-\frac{1}{6\sqrt{3}}\right);\left(\frac{13}{\sqrt{194}},-\frac{5}{\sqrt{194}}\right)$

d)

$\left(\frac{7}{5\sqrt{2}},\frac{1}{5\sqrt{2}}\right);\left(\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right);\left(\frac{13}{\sqrt{194}},-\frac{5}{\sqrt{194}}\right)$

8.

a)

$\left(-3,-5,-4\right);\left(9,4,-3\right);\left(-6,-1,-7\right)$

b)

$\left(-3,-5,-4\right);\left(9,-4,-3\right);\left(6,-1,-7\right)$

c)

$\left(3,-5,-4\right);\left(9,4,-3\right);\left(12,-1,-7\right)$

d)

$\left(3,-5,-4\right);\left(9,4,-3\right);\left(12,1,-7\right)$

9.

a)

$\sqrt{50};\sqrt{104};\sqrt{199}$

b)

$\sqrt{50};\sqrt{104};\sqrt{198}$

c)

$5\sqrt{2};\sqrt{106};\sqrt{198}$

d)

$5\sqrt{2};\sqrt{106};\sqrt{199}$

10.

a)

$\left(\frac{3}{5\sqrt{2}},\frac{-5}{5\sqrt{2}},\frac{-4}{5\sqrt{2}}\right);\left(\frac{9}{\sqrt{106}},\frac{4}{\sqrt{106}},\frac{-3}{\sqrt{106}}\right);\left(\frac{-12}{\sqrt{199}},\frac{-1}{\sqrt{199}},\frac{-7}{\sqrt{199}}\right)$

b)

$\left(\frac{3}{5\sqrt{2}},\frac{-5}{5\sqrt{2}},\frac{-4}{5\sqrt{2}}\right);\left(\frac{9}{\sqrt{106}},\frac{4}{\sqrt{106}},\frac{-3}{\sqrt{106}}\right);\left(\frac{12}{\sqrt{199}},\frac{1}{\sqrt{199}},\frac{-7}{\sqrt{199}}\right)$

c)

$\left(\frac{3}{5\sqrt{2}},\frac{-5}{5\sqrt{2}},\frac{-4}{5\sqrt{2}}\right);\left(\frac{9}{\sqrt{106}},\frac{4}{\sqrt{106}},\frac{-3}{\sqrt{106}}\right);\left(\frac{12}{\sqrt{199}},\frac{-1}{\sqrt{199}},\frac{7}{\sqrt{199}}\right)$

d)

$\left(\frac{3}{5\sqrt{2}},\frac{-5}{5\sqrt{2}},\frac{-4}{5\sqrt{2}}\right);\left(\frac{9}{\sqrt{106}},\frac{4}{\sqrt{106}},\frac{-3}{\sqrt{106}}\right);\left(\frac{12}{\sqrt{199}},\frac{-1}{\sqrt{199}},\frac{-7}{\sqrt{199}}\right)$

11.

Jika

\overrightarrow{a}

= 5i + 12j dan

\overrightarrow{b}

= mi + 13j maka tentukan nilai m agar kedua vektor panjangnya sama

a)

-1

b)

0

c)

1

d)

2

12.

Jika

\overrightarrow{a}

= -8i + 3j dan

\overrightarrow{b}

= -mi + 5j maka tentukan nilai m agar kedua vektor panjangnya sama

a)

$-4\sqrt{3}$

b)

$4\sqrt{3}$

c)

$-16\sqrt{3}$

d)

$16\sqrt{3}$

13.

Jika

\overrightarrow{a}

= -4i + j - k dan

\overrightarrow{b}

= -2mi + 3j - 2k maka tentukan nilai m agar kedua vektor panjangnya sama

a)

-1

b)

0

c)

1

d)

2

14.

Jika

\overrightarrow{a}

= 8i + 2j - k dan

\overrightarrow{b}

= 7i + 3j - mk maka tentukan nilai m agar kedua vektor panjangnya sama

a)

$\sqrt{17}$

b)

$\sqrt{15}$

c)

$\sqrt{13}$

d)

$\sqrt{11}$

15.

Jika titik P (3,-1) dan Q (3,4) sedang R (x,y) terletak pada ruas garis PQ sehingga $\overrightarrow{PR}$ = $\frac{2}{5}\overrightarrow{PQ}$ maka tentukan titik R

a)

(3,1)

b)

(-3,1)

c)

(3,-1)

d)

(-3,-1)

16.

Jika titik P (2,-1) dan Q (-3,4) sedang R (x,y) terletak pada ruas garis PQ sehingga $\overrightarrow{PR}$ = $\frac{2}{5}\overrightarrow{PQ}$ maka tentukan titik R

a)

(0,-1)

b)

(0,1)

c)

(-1,0)

d)

(1,-0)

17.

Jika titik P (2,-3,3) dan Q (2,4,3) sedang R (x,y,z) terletak pada ruas garis PQ sehingga $\overrightarrow{PR}$ = $\frac{5}{7}\overrightarrow{PQ}$ maka tentukan titik R

a)

(3,3,3)

b)

(3,3,2)

c)

(2,2,2

d)

(2,2,3)

18.

Jika titik P (2,3,-1) dan Q (-3,3,4) sedang R (x,y,z) terletak pada ruas garis PQ sehingga $\overrightarrow{PR}$ = $\frac{2}{5}\overrightarrow{PQ}$ maka tentukan titik R

a)

(0,-3,-1)

b)

(0,3,-1)

c)

(0,-3,1)

d)

(0,3,1)

Vektor Mix (28/01/21)

Total questions: 18

Worksheet time: 9mins

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