Few questions concerning vectors, not a clue where to start on these.

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In summary, the conversation involves a student struggling with a vector problem and seeking help. The problem involves finding the equation of a plane and the perpendicular distance from the origin. The conversation suggests using dot product and notes to solve the problem.
  • #1
knowlewj01
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Homework Statement



Ok, so here are the questions, I literally have no idea how to begin on them.

1.Show that the vector 2i+3j+3k is normal to the plane containing the points (1,1,-2), (4,2,-5) and (1,-1,0). Hence find the equation of the plane in the form
(r-a).n(hat)

what is the perpendicular distance from the origin to the plane?There are a couple more questions but i'll take them one at a time.

The Attempt at a Solution



Been looking through my notes for ages and on th internet, can't find anything that makes sense, anyone good with vectors? thanks :)
 
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  • #2
construct aline lying in the plane using two of the given points and dot product it with the line you were given in the question - if they're orthogonal this will vanish.
 

1. What is a vector?

A vector is a mathematical object that has both magnitude and direction. It is often represented as an arrow pointing in a specific direction, with the length of the arrow representing the magnitude of the vector.

2. How is a vector different from a scalar?

A scalar is a mathematical object that only has magnitude, while a vector has both magnitude and direction. Scalars can be represented by a single number, while vectors require multiple components to fully describe them.

3. What are some real-life examples of vectors?

Vectors can be used to represent various physical quantities, such as velocity, force, and displacement. For example, the wind blowing in a specific direction can be represented as a vector, with the direction of the wind as the vector's direction and the wind speed as its magnitude.

4. How are vectors represented mathematically?

Vectors can be represented in several ways, including using coordinates, component form, and magnitude and direction. In coordinate form, the vector is represented by an ordered pair of numbers (x, y). In component form, the vector is represented by its x and y components. In magnitude and direction form, the vector is represented by its magnitude and the angle it makes with a reference axis.

5. What operations can be performed on vectors?

Some common operations on vectors include addition, subtraction, scalar multiplication, and dot product. Addition and subtraction involve combining or subtracting the components of two vectors. Scalar multiplication involves multiplying a vector by a number, which changes its magnitude but not its direction. Dot product is a mathematical operation that results in a scalar value and is used to calculate the angle between two vectors or to project one vector onto another.

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