Domanda del libro di testo
In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit. C = 102°, a = 16 meters, b = 20 meters
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Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 4, Problema 37
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
||w - u||
Guida verificata passo dopo passo1
Identify the vectors given: \( \mathbf{u} = 2\mathbf{i} - 5\mathbf{j} \), \( \mathbf{w} = -\mathbf{i} - 6\mathbf{j} \).
Calculate the vector difference \( \mathbf{w} - \mathbf{u} \) by subtracting the components of \( \mathbf{u} \) from \( \mathbf{w} \):
\[ \mathbf{w} - \mathbf{u} = (-1 - 2)\mathbf{i} + (-6 - (-5))\mathbf{j} \]
Simplify the components to get the resulting vector:
\[ \mathbf{w} - \mathbf{u} = (-3)\mathbf{i} + (-1)\mathbf{j} \]
Find the magnitude (or norm) of the vector \( \mathbf{w} - \mathbf{u} \) using the formula for the length of a vector in 2D:
\[ ||\mathbf{w} - \mathbf{u}|| = \sqrt{(-3)^2 + (-1)^2} \]
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Vector Subtraction
Vector subtraction involves finding the difference between two vectors by subtracting their corresponding components. For vectors u and w, w - u is computed by subtracting each component of u from the corresponding component of w, resulting in a new vector.
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Adding Vectors Geometrically
Magnitude (Norm) of a Vector
The magnitude of a vector is its length in the coordinate plane, calculated using the Pythagorean theorem. For a vector with components (x, y), the magnitude is √(x² + y²). This gives a scalar representing the vector's size.
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Domanda del libro di testo
In Exercises 35–36, the three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree.
A(0, 0), B(-3, 4), C(3, -1)
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Domanda del libro di testo
In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.
B = 125°, a = 8 yards, c = 5 yards
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Domanda del libro di testo
If u = 5i + 2j, v = i - j, and w = 3i - 7j, find u ⋅ (v + w).
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Domanda del libro di testo
In Exercises 33–38, find projᵥᵥ v. Then decompose v into two vectors, v₁ and v₂, where v₁ is parallel to w and v₂ is orthogonal to w.
v = i + 2j, w = 3i + 6j
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Domanda del libro di testo
In Exercises 37–39, find the dot product v ⋅ w. Then find the angle between v and w to the nearest tenth of a degree.
v = 2i + 4j, w = 6i - 11j
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