Question

If the points $(0,1,-2),(3$, $\lambda$,$1)$ and ($\mu$, $7,4$) are collinear, the point on the same line is

• A. $(5,6,3)$
• B. $(1,-1,-2)$
• C. $(-5,-6,-3)$
• D. $(0,0,0)$

Answer 1

Answer: (A)

$(5,6,3)$

The direction vector using the first two points we get $3i+(\lambda -1)j+3k$.

Using the first and third point $\mu i+6j+6k$.

Since they are up to multiplication by a constant we get $\lambda =4$ and $\mu =6$.

Hence direction vector is $i+j+k$.

Any point on the line is given by $(0,1,-2)+t(1,1,1)$. Plugging $t=5$ we get the point $(5,6,3)$.