Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5501 | Determine whether the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
5502 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-5\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ . | 1 |
5503 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~-7\right) $ . | 1 |
5504 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 33 }{ 10 },~0,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 21 }{ 5 },~\dfrac{ 37 }{ 10 },~\dfrac{ 6 }{ 5 }\right) $ . | 1 |
5505 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~6,~7\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
5506 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
5507 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
5508 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
5509 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(0,~5\right) $ . | 1 |
5510 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-7,~3\right) $ and $ \vec{v_2} = \left(-1,~5,~8\right) $ . | 1 |
5511 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~0\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
5512 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
5513 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
5514 | Find the projection of the vector $ \vec{v_1} = \left(-6,~4\right) $ on the vector $ \vec{v_2} = \left(-3,~2\right) $. | 1 |
5515 | Find the projection of the vector $ \vec{v_1} = \left(3,~1,~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~-10,~8\right) $. | 1 |
5516 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~0,~3\right) $ and $ \vec{v_2} = \left(20,~-15,~35\right) $ . | 1 |
5517 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
5518 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~-33,~31\right) $ . | 1 |
5519 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 1 |
5520 | Find the sum of the vectors $ \vec{v_1} = \left(182,~48\right) $ and $ \vec{v_2} = \left(48,~0\right) $ . | 1 |
5521 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
5522 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-10,~2\right) $ . | 1 |
5523 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
5524 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-7,~3\right) $ and $ \vec{v_2} = \left(-1,~5,~8\right) $ . | 1 |
5525 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~2\right) $ and $ \vec{v_2} = \left(-1,~-2,~3\right) $ . | 1 |
5526 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4,~-5\right) $ and $ \vec{v_2} = \left(-4,~8,~10\right) $ . | 1 |
5527 | Find the projection of the vector $ \vec{v_1} = \left(-1,~0,~1\right) $ on the vector $ \vec{v_2} = \left(1,~4,~-4\right) $. | 1 |
5528 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~4\right) $ and $ \vec{v_2} = \left(6,~6,~6 \sqrt{ 2 }\right) $ . | 1 |
5529 | Find the sum of the vectors $ \vec{v_1} = \left(3,~6,~-2\right) $ and $ \vec{v_2} = \left(5,~1,~-4\right) $ . | 1 |
5530 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
5531 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 1 |
5532 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-5\right) $ . | 1 |
5533 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0,~0\right) $ . | 1 |
5534 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $. | 1 |
5535 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-10,~2\right) $ . | 1 |
5536 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~4\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
5537 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
5538 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3,~-4\right) $ . | 1 |
5539 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(8,~-6\right) $. | 1 |
5540 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(-2,~-2,~4\right) $ . | 1 |
5541 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4,~-5\right) $ and $ \vec{v_2} = \left(-45,~-5,~-14\right) $ . | 1 |
5542 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
5543 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~0,~-3\right) $ and $ \vec{v_2} = \left(20,~-15,~35\right) $ . | 1 |
5544 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-4,~-1\right) $ . | 1 |
5545 | Find the difference of the vectors $ \vec{v_1} = \left(3,~6,~-2\right) $ and $ \vec{v_2} = \left(5,~1,~-4\right) $ . | 1 |
5546 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~2\right) $ on the vector $ \vec{v_2} = \left(-1,~0,~1\right) $. | 1 |
5547 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 1 |
5548 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
5549 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~5\right) $ . | 1 |
5550 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |