find the magnitude of vector by scalar and vector A= ? + 4j +4k B= ? + 2j + 3k if the angle between them 15 degrees.
There is some algebra to this..
AdotB=MagA*MagB*costheta
ab+8+12=sqrt[(a^2+14+16)(b^2+4+9)]*cosTheta
which cant be solved, unless a,b are equal where a and b are the i components of each vector. Assuming them the same,
a^2+20=sqrt[(a^2+30)(a^2+13)] * cos15
now square both sides, find a
Vectors are A=ai+4j+4k and B=ai+2J+3k)
To find the magnitude of a vector, we need to calculate the square root of the sum of the squares of its components.
Let's first find the components of vector A and vector B.
Given:
A = ? + 4j + 4k
B = ? + 2j + 3k
Since the component for the x-direction of both vectors is missing, we can assume it to be zero as it will not affect the magnitude calculation.
So, we have:
A = 0i + 4j + 4k
B = 0i + 2j + 3k
Now, we can calculate the magnitude of vector A and vector B using the formula:
|A| = sqrt(Ax^2 + Ay^2 + Az^2)
|B| = sqrt(Bx^2 + By^2 + Bz^2)
For vector A:
|A| = sqrt((0)^2 + (4)^2 + (4)^2)
= sqrt(0 + 16 + 16)
= sqrt(32)
≈ 5.657
Similarly, for vector B:
|B| = sqrt((0)^2 + (2)^2 + (3)^2)
= sqrt(0 + 4 + 9)
= sqrt(13)
≈ 3.606
Please note that the angle between the two vectors does not affect the calculation of their magnitudes.