The angle between two vectors is heta. Part A If heta = 30.0^{circ}, which has the greater magnitude: the scalar product or the vector product of the two vectors? The scalar product and the vector product have equal magnitudes in this case. The vector product has the greater magnitude than the scalar product of the two vectors. The scalar product has the greater magnitude than the vector product of the two vectors. We cannot determine the answer without knowing the magnitudes of the vectors. Part B For what values of heta are the magnitudes of the scalar product and the vector product equal? Express your answers in degrees using three significant figures. Enter positive values from 0^{circ} to 180^{circ} in ascending order
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B = |A||B|cosθ, where |A| and |B| are the magnitudes of the vectors and θ is the angle between them. The vector product (also known as the cross product) is given by the formula AxB = |A||B|sinθ. When θ = 30 degrees, cos30 = √3/2 and sin30 = 1/2. Show more…
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The angle between two vectors is $\theta$. (a) If $\theta=30.0^{\circ}$, which has the greater magnitude: the scalar product or the vector product of the two vectors? (b) For what value (or values) of $\theta$ are the magnitudes of the scalar product and the vector product equal?
Vectors $\vec{A}$ and $\vec{B}$ are in the $x y$ -plane. Vector $\vec{A}$ is in the $+x$ - direction, and the direction of vector $\overrightarrow{\boldsymbol{B}}$ is at an angle $\theta$ from the $+x$ -axis measured toward the $+y$ -axis. (a) If $\theta$ is in the range $0^{\circ} \leq \theta \leq 180^{\circ}$, for what two values of $\theta$ does the scalar product $\vec{A} \cdot \vec{B}$ have its maximum magnitude? For each of these values of $\theta,$ what is the magnitude of the vector product $\vec{A} \times \vec{B} ?(b)$ If $\theta$ is in the range $0^{\circ} \leq \theta \leq 180^{\circ}$ for what value of $\theta$ does the vector product $\vec{A} \times \vec{B}$ have its maximum value? For this value of $\theta,$ what is the magnitude of the scalar product $\vec{A} \cdot \vec{B} ?(\mathrm{c})$ What is the angle $\theta$ in the range $0^{\circ} \leq \theta \leq 180^{\circ}$ for which $\vec{A} \cdot \vec{B}$ is twice $|\vec{A} \times \vec{B}| ?$
Two Vectors Points:30 The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated. DATA: α= 43.9º β= 57.0º |A| = 7.9 cm. The vector A - B is parallel to the -x axis (points due West). Calculate the y-component of vector B. Since the sum vector (A-B) has no y-component, vector A must have the same y-component as vector B. As shown, `east' is for +x, and `north' for +y, thus the answer can be negative. Calculate the x component of the vector A - B . The y and x components of a vector are the projections of the vector onto the corresponding axes. You can draw a triangle and calculate the components by using sin, cos, or tan. Components have signs, + or -
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