Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1901 | Find the projection of the vector $ \vec{v_1} = \left(-2,~2\right) $ on the vector $ \vec{v_2} = \left(0,~-4\right) $. | 2 |
1902 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~2,~-4\right) $ . | 2 |
1903 | Find the projection of the vector $ \vec{v_1} = \left(9,~-7\right) $ on the vector $ \vec{v_2} = \left(-10,~7\right) $. | 2 |
1904 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right) $ . | 2 |
1905 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~6\right) $ . | 2 |
1906 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 2 |
1907 | Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ . | 2 |
1908 | Find the projection of the vector $ \vec{v_1} = \left(15,~30\right) $ on the vector $ \vec{v_2} = \left(-1,~4\right) $. | 2 |
1909 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 2 |
1910 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 2 |
1911 | Find the sum of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(5,~4\right) $ . | 2 |
1912 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~-2\right) $ and $ \vec{v_2} = \left(-5,~8\right) $ . | 2 |
1913 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 2 |
1914 | Find the angle between vectors $ \left(0,~2\right)$ and $\left(2,~1\right)$. | 2 |
1915 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 2 |
1916 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 2 |
1917 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 2 |
1918 | Find the difference of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(5,~4\right) $ . | 2 |
1919 | Find the angle between vectors $ \left(-9,~5\right)$ and $\left(-1,~7\right)$. | 2 |
1920 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 83 }{ 5 },~\dfrac{ 147 }{ 10 }\right) $ . | 2 |
1921 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 2 |
1922 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
1923 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(-1,~0\right)$. | 2 |
1924 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~-6\right) $ and $ \vec{v_2} = \left(-8,~0\right) $ . | 2 |
1925 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~0\right) $ and $ \vec{v_2} = \left(5,~5\right) $ . | 2 |
1926 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(2,~1\right)$. | 2 |
1927 | Find the angle between vectors $ \left(2,~-2\right)$ and $\left(4,~2\right)$. | 2 |
1928 | Find the difference of the vectors $ \vec{v_1} = \left(-15,~40\right) $ and $ \vec{v_2} = \left(-2,~-8\right) $ . | 2 |
1929 | Find the difference of the vectors $ \vec{v_1} = \left(3,~9\right) $ and $ \vec{v_2} = \left(-6,~-7\right) $ . | 2 |
1930 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~-4\right) $ and $ \vec{v_2} = \left(3,~-9\right) $ . | 2 |
1931 | Find the angle between vectors $ \left(3,~2\right)$ and $\left(2,~1\right)$. | 2 |
1932 | Find the difference of the vectors $ \vec{v_1} = \left(8,~0\right) $ and $ \vec{v_2} = \left(-20,~-16\right) $ . | 2 |
1933 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 21 }{ 4 },~7\right) $ . | 2 |
1934 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-4\right) $ and $ \vec{v_2} = \left(-8,~-4\right) $ . | 2 |
1935 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 2 |
1936 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 2 |
1937 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~0\right) $ and $ \vec{v_2} = \left(5,~5\right) $ . | 2 |
1938 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(8,~3\right)$. | 2 |
1939 | Find the angle between vectors $ \left(\dfrac{ 21 }{ 4 },~7\right)$ and $\left(3,~4\right)$. | 2 |
1940 | Find the angle between vectors $ \left(16,~12\right)$ and $\left(33,~23\right)$. | 2 |
1941 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\sqrt{ 3 },~-4\right) $ and $ \vec{v_2} = \left(-1,~4 \sqrt{ 3 }\right) $ . | 2 |
1942 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 2 |
1943 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(3,~-5\right) $ . | 2 |
1944 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-8\right) $ and $ \vec{v_2} = \left(0,~-9\right) $ . | 2 |
1945 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~3\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ . | 2 |
1946 | Find the angle between vectors $ \left(-7,~2\right)$ and $\left(2,~1\right)$. | 2 |
1947 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 2 |
1948 | Find the sum of the vectors $ \vec{v_1} = \left(0.2,~30\right) $ and $ \vec{v_2} = \left(0.2,~120\right) $ . | 2 |
1949 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~8\right) $ . | 2 |
1950 | Find the magnitude of the vector $ \| \vec{v} \| = \left(34,~72\right) $ . | 2 |