Question
Give a mathematical problems for vector quantity
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GPT 3.5
1. Given vectors A = 3i + 4j - 2k and B = 2i - j + 5k, calculate the dot product of A and B.
2. Two forces acting on a body are given by vectors F1 = 2i + 3j - 4k and F2 = -4i + 2j + k. Find the resultant force acting on the body by adding these two vectors.
3. A vector C = 5i - 2j + 3k is perpendicular to vector D = 2i + 4j + 3k. Calculate the scalar product of C and D.
4. A particle moves in a straight line with velocity vector v = (3t)i + (4 - t²)j + (2 + 2t)k, where t is time. Determine the acceleration of the particle.
5. A boat is moving at a velocity vector v = 6i + 2j - 3k with respect to the water. The water is flowing with a velocity vector w = 3i - 2j + 4k with respect to the ground. Find the boat's velocity vector with respect to the ground.
6. The position vector of a particle is given by r(t) = (2t²)i + (4t - 3)j + (t³ - 2)k, where t is time. Determine the velocity and acceleration of the particle.
7. Three parallel forces are acting on a body in the same direction with magnitudes 5N, 7N, and 10N. If the distance between the forces is 2m, what is the resultant force on the body?
2. Two forces acting on a body are given by vectors F1 = 2i + 3j - 4k and F2 = -4i + 2j + k. Find the resultant force acting on the body by adding these two vectors.
3. A vector C = 5i - 2j + 3k is perpendicular to vector D = 2i + 4j + 3k. Calculate the scalar product of C and D.
4. A particle moves in a straight line with velocity vector v = (3t)i + (4 - t²)j + (2 + 2t)k, where t is time. Determine the acceleration of the particle.
5. A boat is moving at a velocity vector v = 6i + 2j - 3k with respect to the water. The water is flowing with a velocity vector w = 3i - 2j + 4k with respect to the ground. Find the boat's velocity vector with respect to the ground.
6. The position vector of a particle is given by r(t) = (2t²)i + (4t - 3)j + (t³ - 2)k, where t is time. Determine the velocity and acceleration of the particle.
7. Three parallel forces are acting on a body in the same direction with magnitudes 5N, 7N, and 10N. If the distance between the forces is 2m, what is the resultant force on the body?