Search problems

3 problems match “vector magnitude”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Dot product with a linear combination ●○○○○ 10 ptsGiven that the angle between vectors $\vec{a}$ and $\vec{b}$ is $120^{\circ}$, and $|\vec{a}|=2$, $|\vec{b}|=5$, find $(2\vec{a}-\vec{b})\cdot\vec{a}$.
2. Area of a parallelogram from vectors ●○○○○ 10 ptsCalculate the area of the parallelogram spanned by the vectors $\vec{a} = (3, -3, 1)$ and $\vec{b} = (4, 9, 2)$. Round to two decimal places.
3. Cosine of angle with orthogonal vector sum ●●○○○ 20 ptsLet $\mathbf{a},$ $\mathbf{b},$ $\mathbf{c}$ be three vectors with equal magnitudes, such that any two of them are orthogonal. If $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{a} + \mathbf{b} + \mathbf{c},$ find $\cos \theta.$ Round to two decimal places.