2x + 3y + 2z = 6

X intercept occurs when y and z = 0, so 2x = 6, x = 3

Y intercept occurs when x and z = 0, so 3y = 6, y = 2

Z intercept occurs when x and y = 0, so 2z = 6, z = 3

For the first question, in vector form, we have:

r = ro + tv

= (4i - 3j + 2k) + t (3i + 2j + 3k)

And for the second question, the line in vector form would be:

= (4i - 3j + 2k) + t (11/4i + -11/3j + 11z)