Collinear Vectors

Q. If $\overrightarrow{a}$ is a vector of magnitude 50 and is collinear with the vector $\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}$ and makes an obtuse angle with the positive direction of z - axis, then $\overrightarrow{a}$ is equal to

1. $24\hat{i}-32\hat{j}-30\hat{k}$
2. $12\hat{i}-16\hat{j}-15\hat{k}$
3. $24\hat{i}+32\hat{j}+30\hat{k}$
4. $12\hat{i}-43\hat{j}-15\hat{k}$

Q. Let a, b and c be three nonzero vectors, no two of which are collinear. If the vector a+2b is collinear with c, and b+3c is collinear with a, then a+2b+6c =

1. $\lambda a$
2. $\lambda b$
3. $\lambda c$
4. $0$

Q. If $\overline{a},\overline{b}$ are the position vectors of $A,B$ respectively and $C$ is a point on $AB$ produced such that $AC=3AB$, then the position vectors of $C$ ?

Q. The vector having magnitude of 12 units in the direction of the $\overrightarrow{A}=3\hat{i}+2\hat{j}-6\hat{k}$
is

1. $36\hat{i}+24\hat{j}-72\hat{k}$
2. $\frac{(36\hat{i}+24\hat{j}-72\hat{k})}{7}$
3. $\frac{(3\hat{i}+2\hat{j}-6\hat{k})}{7}$
4. $12\hat{i}+12\hat{j}-12\hat{k}$