Vectors and Equilibrium
What is the angle between the vector $\vec{A} = \hat{i} + \hat{j}$ and the x-axis?
A) $0^\circ$
B) $45^\circ$
C) $90^\circ$
D) $180^\circ$
If the dot product of two vectors is equal to the product of their magnitudes, the vectors are:
A) Perpendicular
B) Parallel
C) Anti-parallel
D) Null vectors
The center of gravity is the point at which the total gravitational force acts. For a symmetrical body, it is usually located at:
A) The edge
B) The center
C) The corner
D) Outside the body
Which of the following is not a condition of equilibrium?
A) Sum of all forces is zero
B) Sum of all torques is zero
C) The body is at rest
D) The body has no angular acceleration
A vector that can be shifted parallel to itself without changing its properties is a:
A) Free vector
B) Localized vector
C) Position vector
D) Null vector
The scalar product of a vector with itself is:
A) $\vec{A} \cdot \vec{A} = A^2$
B) $\vec{A} \cdot \vec{A} = 0$
C) $\vec{A} \times \vec{A} = A^2$
D) $\vec{A} \times \vec{A} = 0$
The cross product of a vector with itself is:
A) $\vec{A} \cdot \vec{A} = A^2$
B) $\vec{A} \cdot \vec{A} = 0$
C) $\vec{A} \times \vec{A} = A^2$
D) $\vec{A} \times \vec{A} = 0$
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