គេមានសមីការប៉ារ៉ាម៉ែតនៃបន្ទាត់ ( L ) : x = 7 − 2 t , y = − 6 + t , z = 1 + 5 t , ( t ∈ R ) \left(L\right):\ x=7-2t,\ \ y=-6+t\ ,\ z=1+5t\ ,\ \left(t\in R\right) ( L ) : x = 7 − 2 t , y = − 6 + t , z = 1 + 5 t , ( t ∈ R ) ចូររកវ៉ិចទ័រប្រាប់ទិសនៃបន្ទាត់ ( L ) \left(L\right) ( L ) ។

u → = ( − 2 , 1 , 5 ) \overrightarrow{u\ }=\left(-2,\ 1,\ 5\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( − 2 , 1 , 5 )

u → = ( 7 , − 6 , 1 ) \overrightarrow{u\ }=\left(7,\ -6,\ 1\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 7 , − 6 , 1 )

u → = ( 5 , − 5 , 6 ) \overrightarrow{u\ }=\left(5,\ -5,\ 6\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 5 , − 5 , 6 )

u → = ( 2 , 1 , 5 ) \overrightarrow{u\ }=\left(2,\ 1,\ 5\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 , 1 , 5 )

គេមានសមីការប្លង់ ( P ) : 2 x − y + z − 3 = 0 \left(P\right):\ 2x-y+z-3=0 ( P ) : 2 x − y + z − 3 = 0 ។ ចូររកកូអរដោនេនៃវ៉ិចទ័រណ័រម៉ាល់នៃប្លង់ ( P ) \left(P\right) ( P ) ។

v → = ( 2 , − 1 , 1 ) \overrightarrow{v\ }=\left(2,\ -1,\ 1\right) v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 , − 1 , 1 )

v → = ( 2 , 1 , 1 ) \overrightarrow{v\ }=\left(2\ ,\ 1,\ 1\ \right) v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 , 1 , 1 )

v → = 2 i → + j → + k → \overrightarrow{v\ }=2\overrightarrow{i\ }+\overrightarrow{j\ \ }+\overrightarrow{k\ \ } v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = 2 i <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> + j <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> + k <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

v → = ( 2 , − 1 , 3 ) \overrightarrow{v\ \ }=\left(2,\ -1,\ 3\right) v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 , − 1 , 3 )

Quiz1 Semester 2:

Authored by Sothea Ly

Mathematics

11th - 12th Grade

Used 1+ times

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

គេមានសមីការប៉ារ៉ាម៉ែតនៃបន្ទាត់ $\left(L\right):\ x=7-2t,\ \ y=-6+t\ ,\ z=1+5t\ ,\ \left(t\in R\right)$ ចូររកវ៉ិចទ័រប្រាប់ទិសនៃបន្ទាត់ $\left(L\right)$ ។

$\overrightarrow{u\ }=\left(-2,\ 1,\ 5\right)$

$\overrightarrow{u\ }=\left(7,\ -6,\ 1\right)$

$\overrightarrow{u\ }=\left(5,\ -5,\ 6\right)$

$\overrightarrow{u\ }=\left(2,\ 1,\ 5\right)$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

គេមានសមីការប្លង់ $\left(P\right):\ 2x-y+z-3=0$ ។

ចូររកកូអរដោនេនៃវ៉ិចទ័រណ័រម៉ាល់នៃប្លង់ $\left(P\right)$ ។

$\overrightarrow{v\ }=\left(2\ ,\ 1,\ 1\ \right)$

$\overrightarrow{v\ }=\left(2,\ -1,\ 1\right)$

$\overrightarrow{v\ }=2\overrightarrow{i\ }+\overrightarrow{j\ \ }+\overrightarrow{k\ \ }$

$\overrightarrow{v\ \ }=\left(2,\ -1,\ 3\right)$

OPEN ENDED QUESTION

10 mins • Ungraded

គេឲ្យបីចំណុច $R\left(2\ ,-\ 2\ ,-1\right)\ ,\ S\left(2\ ,\ 1\ ,\ 2\right)\$ និង $T\left(1\ ,\ 2,\ -1\right)$ ។

ក. ចូរគណនា $\overrightarrow{RS}\ ,\ \left|\overrightarrow{RS}\right|\$ និង $\overrightarrow{ST\ }$ ។

ខ. ចូរសេរសេរសមីការប៉ារ៉ាម៉ែតនៃបន្ទាត់ $RS$ ។
គ. ចូររកវ៉ិចទ័រណ័រម៉ាល់នៃប្លង់កាត់តាមចំណុច $R,\ S\ ,\ T$ រួចសរសេរសមីការប្លង់ $RST$ ។

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OPEN ENDED QUESTION

3 mins • Ungraded

គេឲ្យបីចំណុច $A\left(4\ ,\ 2\ ,-1\right)\ ,\ B\left(2\ ,\ 1\ ,\ 5\right)$ និង $C\left(9,\ 4,\ 1\right)$ ។

a. បង្ហាញថា $\overrightarrow{AB}$ កែង $\overrightarrow{AC\ }$ ។

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OPEN ENDED QUESTION

15 mins • Ungraded

គេឲ្យបីចំណុច $A\left(4\ ,\ 2\ ,-1\right)\ ,\ B\left(2\ ,\ 1\ ,\ 5\right)$ និង $C\left(9,\ 4,\ 1\right)$ ។

ចូរសរសេរសមីការប្លង់កាត់តាម 3 ចំណុច $A,\ B\ ,\ C$ រួចរកចម្ងាយពីចំណុច $D\left(8\ ,\ 1\ ,\ 0\ \right)$ ទៅប្លង់ $ABC$ ។

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OPEN ENDED QUESTION

10 mins • Ungraded

គេឲ្យពីរចំណុច $A\left(4\ ,\ 2\ ,-1\right)\$ និង $B\left(2,\ 1,\ 5\right)$ ។

ចូរសរសេរសមីការបន្ទាត់កាត់តាមចំណុច $A$ និង $B$ ។

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OPEN ENDED QUESTION

15 mins • Ungraded

រកសមីការបន្ទាត់ $\left(m\right)$ ដែលបានមកពីប្រសព្វរវាងប្លង់ $\left(P\right):\ 2x-y+2z-6=0$ និង $\left(Q\right):\ x-2y+2z+3=0$ ។

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Quiz1 Semester 2:

គេមានសមីការប្លង់ (P): 2x−y+z−3=0\left(P\right):\ 2x-y+z-3=0(P): 2x−y+z−3=0 ។ចូររកកូអរដោនេនៃវ៉ិចទ័រណ័រម៉ាល់នៃប្លង់ (P)\left(P\right)(P) ។

គេឲ្យពីរចំណុច A(4 , 2 ,−1) A\left(4\ ,\ 2\ ,-1\right)\ A(4 , 2 ,−1) និង B(2, 1, 5)B\left(2,\ 1,\ 5\right)B(2, 1, 5) ។ចូរសរសេរសមីការបន្ទាត់កាត់តាមចំណុច AA និង BBB ។

រកសមីការបន្ទាត់ (m)\left(m\right)(m) ដែលបានមកពីប្រសព្វរវាងប្លង់ (P): 2x−y+2z−6=0\left(P\right):\ 2x-y+2z-6=0(P): 2x−y+2z−6=0 និង (Q): x−2y+2z+3=0\left(Q\right):\ x-2y+2z+3=0(Q): x−2y+2z+3=0 ។

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គេមានសមីការប្លង់ $\left(P\right):\ 2x-y+z-3=0$ ។

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រកសមីការបន្ទាត់ $\left(m\right)$ ដែលបានមកពីប្រសព្វរវាងប្លង់ $\left(P\right):\ 2x-y+2z-6=0$ និង $\left(Q\right):\ x-2y+2z+3=0$ ។