Anyone able to help with these vectors geometry and planes questions?

In summary, a vector has both magnitude and direction, while a scalar only has magnitude. The magnitude of a vector can be found by taking the square root of the sum of the squares of its components. The dot product of two vectors is a single number calculated by multiplying corresponding components and adding them together. To determine if two vectors are parallel, their directions must be the same or opposite, and their magnitudes must be proportional. Alternatively, the dot product of the two vectors will equal the product of their magnitudes. The equation of a plane in 3-dimensional space can be written as Ax + By + Cz + D = 0, where A, B, and C are coefficients and D is a constant, representing all points that
  • #1
Carlito
1
0
Can anyone help me with parts (b) and (c) of this question: http://203.219.144.182/carl/q1ii.gif


I've done parts (i) and (ii) but can anyone help with parts (iii) and (iv)
http://203.219.144.182/carl/q2.gif

answers for parts (i) and (ii):
http://203.219.144.182/carl/q2a.jpg


Thanks heaps, it is really important and kinda urgent.
 
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  • #2
b) You should use the cosine-formula to express thess these lengths.
Also, remember the relation between the inner product, vector lengths, and the cosine of the angle between the two vectors.
c) Ought to follow easily from b)
 
  • #3


Sure, I'd be happy to help with your geometry and planes questions. Can you please provide more specific information about what you need help with for parts (b) and (c) of the first question and parts (iii) and (iv) of the second question? It would also be helpful if you could provide your attempted solutions or any specific areas you are struggling with so I can better assist you. Additionally, please make sure to include any relevant diagrams or equations that may be needed to solve the problems. Looking forward to helping you out!
 

FAQ: Anyone able to help with these vectors geometry and planes questions?

What is the difference between a vector and a scalar?

A vector is a quantity that has both magnitude (size) and direction, while a scalar is a quantity that only has magnitude.

How do you find the magnitude of a vector?

The magnitude of a vector can be found by taking the square root of the sum of the squares of its components. In other words, if a vector has components (a, b, c), its magnitude is √(a² + b² + c²).

What is the dot product of two vectors?

The dot product of two vectors is a single number that is calculated by multiplying the corresponding components of the two vectors and then adding them together. It is used to determine the angle between two vectors and can also be used to project one vector onto another.

How do you determine if two vectors are parallel?

If two vectors are parallel, their direction will be the same or opposite and their magnitudes will be proportional. This means that one vector can be multiplied by a constant to equal the other vector. Alternatively, the dot product of the two vectors will be equal to the product of their magnitudes.

What is the equation of a plane in 3-dimensional space?

The equation of a plane in 3-dimensional space can be written as Ax + By + Cz + D = 0, where A, B, and C are the coefficients for the x, y, and z variables, and D is a constant. This equation represents all the points (x, y, z) that lie on the plane.

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