calculate the absolute value of the vector z=u+v if u=i-j and v=2i+4j.
We have to find the absolute value of the vector z = u + v if u = i - j and v = 2i + 4j.
z = u + v
=> z = i - j + 2i + 4j
add the terms with i and those with j
=> z = 3i + 3j
The absolute value of z = 3i + 3j is
sqrt ( 3^2 + 3^2)
=> sqrt (2*9)
=> 3 sqrt 2
Therefore the required absolute value of the vector z is 3*sqrt 2.
To find the absolute value of z = u+v.
u = i-j.
v = 2i+4j.
Therefore u+v = (i-j)+(2i+4j) =
z = i-j+2i+4j
z = (i+2i)+(-j+4j)
z = 3i+3j.
|z| = (3^(2)+3^2)^(1/2)
|z| = 3 sqrt2 is the absolute value of z.
The modulus of a vector has the formula:
|z| = sqrt (x^2 + y^2), where x and y are the coefficients of the unit vectors i and j.
First, we'll determine the vector z:
z = u + v
z = i - j + 2i + 4j
z = 3i + 3j
We'll identify the coefficients x and y: x = y = 3
We'll calculate the absolute value of z:
|z| = sqrt (3^2 + 3^2)
|z| = sqrt (9 + 9)
|z| = 3 sqrt 2