Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1551 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 2 |
1552 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~4\right) $ and $ \vec{v_2} = \left(4 \sqrt{ 2 },~4,~4\right) $ . | 2 |
1553 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~6\right) $ . | 2 |
1554 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~40\right) $ . | 2 |
1555 | Find the magnitude of the vector $ \| \vec{v} \| = \left(14,~4\right) $ . | 2 |
1556 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 2 |
1557 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(7,~5\right) $ . | 2 |
1558 | Find the sum of the vectors $ \vec{v_1} = \left(6,~3,~4 \sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(6,~0,~10 \sqrt{ 5 }\right) $ . | 2 |
1559 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(0,~-\dfrac{ 1 }{ 2 }\right) $ . | 2 |
1560 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-1\right) $ . | 2 |
1561 | Find the angle between vectors $ \left(80,~0\right)$ and $\left(170,~0\right)$. | 2 |
1562 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 2 |
1563 | Find the sum of the vectors $ \vec{v_1} = \left(0,~-32\right) $ and $ \vec{v_2} = \left(6,~-185\right) $ . | 2 |
1564 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~9\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 2 |
1565 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ . | 2 |
1566 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~-1\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 2 |
1567 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1568 | Find the sum of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-6,~0\right) $ . | 2 |
1569 | Find the sum of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 2 |
1570 | Find the difference of the vectors $ \vec{v_1} = \left(4,~14\right) $ and $ \vec{v_2} = \left(24,~0\right) $ . | 2 |
1571 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~\dfrac{ 31 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 22 }{ 5 },~\dfrac{ 73 }{ 10 }\right) $ . | 2 |
1572 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 3 }}{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ . | 2 |
1573 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~8\right) $ . | 2 |
1574 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3\right) $ . | 2 |
1575 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 2 |
1576 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~9\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 2 |
1577 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-2\right) $ . | 2 |
1578 | Find the angle between vectors $ \left(0,~0,~45\right)$ and $\left(\dfrac{ 95373 }{ 10000 },~0,~\dfrac{ 95373 }{ 10000 }\right)$. | 2 |
1579 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11.6881,~32.6073\right) $ . | 2 |
1580 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~3,~14 \sqrt{ 5 }\right) $ . | 2 |
1581 | Find the angle between vectors $ \left(-7,~8\right)$ and $\left(5,~3\right)$. | 2 |
1582 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 2 |
1583 | Determine whether the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 2 |
1584 | Find the sum of the vectors $ \vec{v_1} = \left(11.6881,~32.6073\right) $ and $ \vec{v_2} = \left(7.8137,~6.5564\right) $ . | 2 |
1585 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(1,~-6\right) $ . | 2 |
1586 | Find the angle between vectors $ \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right)$ and $\left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right)$. | 2 |
1587 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~12\right) $ . | 2 |
1588 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 2 |
1589 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 2 |
1590 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 2 |
1591 | Find the angle between vectors $ \left(-21.58,~-20.84\right)$ and $\left(-9.72,~-20.85\right)$. | 2 |
1592 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 2 |
1593 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1594 | Calculate the dot product of the vectors $ \vec{v_1} = \left(240,~310\right) $ and $ \vec{v_2} = \left(\dfrac{ 14 }{ 5 },~\dfrac{ 74 }{ 25 }\right) $ . | 2 |
1595 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 3 }}{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ . | 2 |
1596 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-2\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ . | 2 |
1597 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-3\right) $ . | 2 |
1598 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~12\right) $ . | 2 |
1599 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ . | 2 |
1600 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |