he magnitude (or length) of vector $\\vec{v}$.","points":1},{"id":"4d528106-0b30-4a92-9309-8aea596b8f67","cardType":"basic","front":"In the column vector $\\begin{pmatrix} x \\\\ y \\end{pmatrix}$, what do the numbers represent?","back":"

$x$: horizontal component
$y$: vertical component

","points":2},{"id":"fc86e841-d9ef-4674-88f0-6761f44a9e8c","cardType":"basic","front":"If $\\vec{AB} = \\begin{pmatrix} 5 \\\\ -2 \\end{pmatrix}$, what is $\\vec{BA}$?","back":"$$\\begin{pmatrix} -5 \\\\ 2 \\end{pmatrix}$","points":1},{"id":"2e37c016-6f8b-461c-a557-3299e2e88c2d","cardType":"cloze","front":"The magnitude of a vector $\\vec{v} = \\begin{pmatrix} x \\\\ y \\end{pmatrix}$ is calculated using the formula $|\\vec{v}| = \\text{[...]}$.","back":"The magnitude of a vector $\\vec{v} = \\begin{pmatrix} x \\\\ y \\end{pmatrix}$ is calculated using the formula $|\\vec{v}| = \\boxed{\\sqrt{x^2+y^2}}$.","points":null},{"id":"0a5310bc-3ee2-46af-8c6b-f639d77ce053","cardType":"basic","front":"Why is the magnitude of a vector always positive, even if components are negative?","back":"Negative components square to positives: $(-x)^2 = x^2$.","points":2},{"id":"c1ed8f93-2bd4-45e0-87c5-4f97492ba63e","cardType":"cloze","front":"To reverse a vector, you must change the [ ] of both components.","back":"To reverse a vector, you must change the signs of both components.","points":null},{"id":"1a27c7a4-c9ef-40aa-b2ca-2ce61dd130ce","cardType":"basic","front":"State a vector path to find $\\vec{AC}$ using the point $B$.","back":"$$\\vec{AC} = \\vec{AB} + \\vec{BC}$","points":1},{"id":"7ffc9d6a-bb08-47a9-85f5-76fd595dad85","cardType":"basic","front":"How is $\\vec{BC}$ expressed in terms of $\\vec{AC}$ and $\\vec{AB}$?","back":"$$\\vec{BC} = \\vec{AC} - \\vec{AB}$","points":2},{"id":"7872b4ce-568a-44e1-9c10-6216b2a8e00b","cardType":"basic","front":"Calculate the magnitude of $\\vec{v} = \\begin{pmatrix} -8 \\\\ 15 \\end{pmatrix}$.","back":"17","points":2},{"id":"06633ca2-323c-4f4c-ac45-fb4640e69810","cardType":"basic","front":"What defines an exact magnitude in vector geometry?","back":"An answer that has not been rounded, typically written as a surd.","points":1},{"id":"d8d36c26-3647-4f88-aec8-2b17b735627f","cardType":"cloze","front":"To simplify a magnitude like $\\sqrt{116}$, you should identify and factor out [ ] (e.g., 4, 9, 16).","back":"To simplify a magnitude like $\\sqrt{116}$, you should identify and factor out square factors (e.g., 4, 9, 16).","points":null},{"id":"5cf3d69d-0f07-401e-8c1c-b9c33ce3083d","cardType":"basic","front":"Simplify the magnitude $\\sqrt{116}$ into a simplified surd.","back":"$$2\\sqrt{29}$","points":2},{"id":"0f3d726b-48c5-484b-84c7-73c9b58f85d9","cardType":"basic","front":"If $\\vec{AB} = \\begin{pmatrix} 3 \\\\ 4 \\end{pmatrix}$ and $\\vec{DC} = 3\\vec{AB}$, find the column vector for $\\vec{DC}$.","back":"$$\\begin{pmatrix} 9 \\\\ 12 \\end{pmatrix}$","points":1},{"id":"9c96f8ba-15de-4ec5-a063-d56c0f1ddf21","cardType":"basic","front":"In a parallelogram $ABCD$, describe the vector path for the diagonal $\\vec{AC}$.","back":"$$\\vec{AC} = \\vec{AB} + \\vec{BC}$","points":1},{"id":"799f7a7a-fbc7-4342-9b8d-039074fa0458","cardType":"basic","front":"Find the magnitude of $\\vec{v} = \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}$.","back":"$$\\sqrt{13}$","points":1},{"id":"edf34346-4303-4fbd-a879-ecccde027742","cardType":"basic","front":"Outline the two-stage method for finding the magnitude of a hidden vector in geometry.","back":"

1. Find the column vector using a path.
2. Apply the Pythagoras formula $\\sqrt{x^2+y^2}$.

","points":2},{"id":"2c9f64c6-86ee-41c0-82a7-226c114a6bfa","cardType":"cloze","front":"A

The Magnitude of a Vector Flashcards

The Magnitude of a Vector Flashcards

The Magnitude of a Vector Flashcards

The Magnitude of a Vector Flashcards