Question

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

a = 2i + 3j + k and b = i - 2j + k

Answer 1

is the answer 5( a/root a^2 + b^2 + c^2)?

Answer 2

find the unit vector along a+b,
then multiply it by 5

Answer 3

parallel vectors have x1/x2 = y1/y2 = z1/z2

Answer 4

a = 2i + 3j + k
b = i - 2j + k
--------------------
a+b = 3i + j + 2k

Answer 5

thats the resultant of a and b, right ?

Answer 6

oh okay so first I find a+b's unit vector, multiply with 5.. that's the magnitude..

To find if the vectors are parallel, I put its direction ratios in the form of x1/x2 = y1/y2 = z1/z2

if its equal, its parallel.. Am I right?

Answer 7

thats right, but we can look at it another way :
since you're just multiplying by 5, which is a scalar, the vector will be parallel to the unit vector anyways.

Answer 8

soo unit vector is..



3/root14, 1/root14, 2/root14

multiplied by 5 = 15/root14, 5/roo14, 10/root14