Answer: To find a vector parallel to u = -4i + 3j + 6k and with magnitude ||v|| = 4, we can use the formula:
v = (||v|| / ||u||) u
where u is the given vector and ||u|| is its magnitude.
First, we find the magnitude of u:
||u|| = sqrt((-4)^2 + 3^2 + 6^2) = sqrt(61)
Then, we plug in the values to get:
v = (4 / sqrt(61)) (-4i + 3j + 6k)
Multiplying out, we get:
v = (-16/sqrt(61))i + (12/sqrt(61))j + (24/sqrt(61))k
Therefore, the vector v parallel to u = -4i + 3j + 6k and with a magnitude ||v|| = 4 is:
v = (-16/sqrt(61))i + (12/sqrt(61))j + (24/sqrt(61))k.
Explanation: