กำหนดให้ a → = − 8 i + 4 j − 2 k \overrightarrow{a}=-8i+4j-2k a <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"> = − 8 i + 4 j − 2 k b → = 5 i − 4 j + 7 k \overrightarrow{b}=5i-4j+7k b <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 i − 4 j + 7 k จงหา a → + b → \overrightarrow{a}+\overrightarrow{b} a <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"> + b <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">

− 3 i + 5 k -3i+5k − 3 i + 5 k

− 13 i + 8 j − 9 k -13i+8j-9k − 1 3 i + 8 j − 9 k

− 3 i + 8 j + 5 k -3i+8j+5k − 3 i + 8 j + 5 k

กำหนดให้ a → = − 8 i + 4 j − 2 k \overrightarrow{a}=-8i+4j-2k a <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"> = − 8 i + 4 j − 2 k b → = 5 i − 4 j + 7 k \overrightarrow{b}=5i-4j+7k b <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 i − 4 j + 7 k จงหา a → − b → \overrightarrow{a}-\overrightarrow{b} a <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"> − b <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">

− 13 i + 8 j − 9 k -13i+8j-9k − 1 3 i + 8 j − 9 k

− 3 i + 5 k -3i+5k − 3 i + 5 k

− 3 i + 8 j + 5 k -3i+8j+5k − 3 i + 8 j + 5 k

กำหนดให้ a → = − 4 i + 3 j − 5 k \overrightarrow{a}=-4i+3j-5k a <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"> = − 4 i + 3 j − 5 k b → = 2 i + 6 j − 2 k \overrightarrow{b}=2i+6j-2k b <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 + 6 j − 2 k จงหา a → × b → \overrightarrow{a}\times\overrightarrow{b} a <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"> × b <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">

24 i − 18 j − 30 k 24i-18j-30k 2 4 i − 1 8 j − 3 0 k

− 36 i − 18 j − 30 k -36i-18j-30k − 3 6 i − 1 8 j − 3 0 k

24 i + 18 j + 30 k 24i+18j+30k 2 4 i + 1 8 j + 3 0 k

− 36 + 18 j + 30 k -36+18j+30k − 3 6 + 1 8 j + 3 0 k

บทที่ 1 ปริมาณเวกเตอร์

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Hard

Sasori Akasuna-no

Used 2+ times

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5 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

จงหาขนาดของเวกเตอร์ $\overrightarrow{a}=12i+16j$

$10$ หน่วย

$20$ หน่วย

$30$ หน่วย

$40$ หน่วย

MULTIPLE CHOICE QUESTION

1 min • 1 pt

กำหนดให้ $\overrightarrow{a}=-8i+4j-2k$
$\overrightarrow{b}=5i-4j+7k$

จงหา $\overrightarrow{a}+\overrightarrow{b}$

$3i-5k$

$-13i+8j-9k$

$-3i+5k$

$-3i+8j+5k$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

กำหนดให้ $\overrightarrow{a}=-8i+4j-2k$
$\overrightarrow{b}=5i-4j+7k$

จงหา $\overrightarrow{a}-\overrightarrow{b}$

$3i-5k$

$-13i+8j-9k$

$-3i+5k$

$-3i+8j+5k$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

กำหนดให้ $\overrightarrow{a}=-4i+3j-5k$
$\overrightarrow{b}=2i+6j-2k$

จงหา $\overrightarrow{a}\cdot\overrightarrow{b}$

$5$ หน่วย

$10$ หน่วย

$15$ หน่วย

$20$ หน่วย

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

กำหนดให้    $\overrightarrow{a}=-4i+3j-5k$
   $\overrightarrow{b}=2i+6j-2k$

จงหา $\overrightarrow{a}\times\overrightarrow{b}$

$24i-18j-30k$

$-36i-18j-30k$

$24i+18j+30k$

$-36+18j+30k$

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บทที่ 1 ปริมาณเวกเตอร์

5 questions

จงหาขนาดของเวกเตอร์ a→=12i+16j\overrightarrow{a}=12i+16ja=12i+16j

กำหนดให้ a→=−8i+4j−2k\overrightarrow{a}=-8i+4j-2ka=−8i+4j−2k b→=5i−4j+7k\overrightarrow{b}=5i-4j+7kb=5i−4j+7k จงหา a→+b→\overrightarrow{a}+\overrightarrow{b}a+b

กำหนดให้ a→=−8i+4j−2k\overrightarrow{a}=-8i+4j-2ka=−8i+4j−2k b→=5i−4j+7k\overrightarrow{b}=5i-4j+7kb=5i−4j+7k จงหา a→−b→\overrightarrow{a}-\overrightarrow{b}a−b

กำหนดให้ a→=−4i+3j−5k\overrightarrow{a}=-4i+3j-5ka=−4i+3j−5k b→=2i+6j−2k\overrightarrow{b}=2i+6j-2kb=2i+6j−2k จงหา a→⋅b→\overrightarrow{a}\cdot\overrightarrow{b}a⋅b

กำหนดให้ a→=−4i+3j−5k\overrightarrow{a}=-4i+3j-5ka=−4i+3j−5k b→=2i+6j−2k\overrightarrow{b}=2i+6j-2kb=2i+6j−2k จงหา a→×b→\overrightarrow{a}\times\overrightarrow{b}a×b

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จงหาขนาดของเวกเตอร์ $\overrightarrow{a}=12i+16j$

กำหนดให้ $\overrightarrow{a}=-8i+4j-2k$
$\overrightarrow{b}=5i-4j+7k$

จงหา $\overrightarrow{a}+\overrightarrow{b}$

กำหนดให้ $\overrightarrow{a}=-8i+4j-2k$
$\overrightarrow{b}=5i-4j+7k$

จงหา $\overrightarrow{a}-\overrightarrow{b}$

กำหนดให้ $\overrightarrow{a}=-4i+3j-5k$
$\overrightarrow{b}=2i+6j-2k$

จงหา $\overrightarrow{a}\cdot\overrightarrow{b}$

กำหนดให้ $\overrightarrow{a}=-4i+3j-5k$
$\overrightarrow{b}=2i+6j-2k$

จงหา $\overrightarrow{a}\times\overrightarrow{b}$