Determine the vector having initial point P(x¡,y¡,z¡) and the terminal point Q(x¡¡,y¡¡,z¡¡) and find its magnitude.
For P(a,b,c) and Q(d,e,f)
vector PQ = (d-a,e-b,f-c)
magnitude of vector PQ = √((d-a)^2 + (e-b)^2 + (f-c)^2)
Vector u has an initial point (3,3) and a terminal point (7,2) find the magnitude of u
Oh, we're going on a vector adventure! Alrighty then! So, to find the vector from point P(x¡, y¡, z¡) to point Q(x¡¡, y¡¡, z¡¡), we need to subtract the coordinates of P from the coordinates of Q.
Now, let's do some number crunching. The vector V is given by V = Q - P.
So, the x-component of V is x¡¡ - x¡, the y-component of V is y¡¡ - y¡, and the z-component of V is z¡¡ - z¡.
But wait, that's not all! We need to find the magnitude of this vector too. To do that, we need to use the Pythagorean theorem.
The magnitude of V is calculated as the square root of the sum of the squares of its components. Mathematically, it can be expressed as follows:
|V| = sqrt((x¡¡ - x¡)^2 + (y¡¡ - y¡)^2 + (z¡¡ - z¡)^2)
There you have it! You now know how to find the vector from point P to point Q and its magnitude. Happy vector-ing!
To determine the vector from the initial point P(x¡, y¡, z¡) to the terminal point Q(x¡¡, y¡¡, z¡¡), we subtract the coordinates of the initial point from the coordinates of the terminal point.
The vector can be represented as:
v = Q - P
To find the magnitude of the vector, we use the formula:
|v| = √(x^2 + y^2 + z^2)
Let's calculate the vector and its magnitude:
v = (x¡¡ - x¡, y¡¡ - y¡, z¡¡ - z¡)
|v| = √((x¡¡ - x¡)^2 + (y¡¡ - y¡)^2 + (z¡¡ - z¡)^2)
To determine the vector with the initial point P(x¡,y¡,z¡) and the terminal point Q(x¡¡,y¡¡,z¡¡), we need to subtract the coordinates of the initial point from the coordinates of the terminal point.
The vector can be represented as: V = Q - P.
The components of the vector V are:
Vx = x¡¡ - x¡
Vy = y¡¡ - y¡
Vz = z¡¡ - z¡
To find the magnitude (or length) of the vector, we use the formula:
Magnitude = ||V|| = sqrt(Vx^2 + Vy^2 + Vz^2)
Let's calculate the vector components and magnitude using this formula.