What is the distance between the two points A(1, 2, 3) and B(4, -2, 3) in three-dimensional Cartesian space?
Answer and explanation
Correct answer: B. 5
The distance formula in R^3 is d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2). Substituting coordinates: d = sqrt((4 - 1)^2 + (-2 - 2)^2 + (3 - 3)^2) = sqrt(3^2 + (-4)^2 + 0^2) = sqrt(9 + 16 + 0) = sqrt(25) = 5.
Practise more Integral Calculus, Analytic Geometry, Statistics, and Medical Physics.
Free questions with an explanation for every one, and full timed Toelatingsexamen Arts & Tandarts België (Medical & Dental Entrance Exam) mock tests.
More Integral Calculus, Analytic Geometry, Statistics, and Medical Physics questions
- What is the value of the definite integral integral_{0}^{1} x * e^(x^2) dx?
- Using integration by parts, what is the antiderivative of f(x) = x * cos(x)?
- What is the volume of the solid of revolution formed by rotating the region under the curve y = sqrt(x) from x = 0 to x = 4 around the x-axi…
- In clinical pharmacokinetics, a drug is eliminated via first-order kinetics with an elimination rate constant ke = 0.1386 h^-1. If the initi…
- What is the center and radius of the circle defined by the equation x^2 + y^2 - 6x + 8y = 0?
- What is the perpendicular distance from the point P(2, 3) to the straight line given by the equation 3x + 4y - 8 = 0?