Find the resolved part of the question.i+3j-2k in the direction of the vector 2i+4j+k

To find the resolved part (or the component) of the vector A = i + 3j - 2k in the direction of the vector B = 2i + 4j + k, we use the formula for the projection of one vector onto another:

Resolved part of A in the direction of B = (A · B) / |B|

Step 1: Compute the dot product A · B
The dot product of two vectors A and B is given by:

A · B = (1 * 2) + (3 * 4) + (-2 * 1)
= 2 + 12 - 2
= 12

Step 2: Compute the magnitude of B
The magnitude of vector B = |B| is given by:

|B| = sqrt((2)^2 + (4)^2 + (1)^2)
= sqrt(4 + 16 + 1)
= sqrt(21)

Step 3: Compute the resolved part
Resolved part = (A · B) / |B|
= 12 / sqrt(21)

Thus, the resolved part of the vector i + 3j - 2k in the direction of 2i + 4j + k is 12 / sqrt(21).