Practise five conversions between vector and Cartesian forms

Self-Practice 7:

(a) Convert $\mathbf r=(2,3,-1)+\lambda(3,4,5)$, λ real, to Cartesian form.

(b) Convert $\mathbf r=\mathbf i+\mathbf j+\lambda(\mathbf i+5\mathbf k)$, λ real, to Cartesian form.

(c) Convert $(x-1)/2=y/3=z-4$ to a vector equation.

(d) Convert $(1-x)/3=(2y-1)/5$, z=4, to a vector equation.

(e) Give vector and Cartesian equations for the line through A with position vector $\mathbf a=\mathbf i-3\mathbf j+2\mathbf k$, parallel to $\mathbf m=5\mathbf i+4\mathbf j-\mathbf k$.