Relative to the origin $O$, the points $A$, $B$, $C$ have position vectors $5\mathbf{i}+4\mathbf{j}+

Question

Relative to the origin $O$, the points $A$, $B$, $C$ have position vectors $5\mathbf{i}+4\mathbf{j}+10\mathbf{k}$, $-4\mathbf{i}+4\mathbf{j}-2\mathbf{k}$ and $-5\mathbf{i}+9\mathbf{j}+5\mathbf{k}$ respectively. Find the cartesian equation of the line $AB$. [2] Find the length of projection of the vector $\overrightarrow{AC}$ on line $AB$. [2] Find the position vector of the foot of the perpendicular,$N$, from $C$ to line $AB$. [3] The point $D$ lies on the line $CN$ produced and is such that $N$ is the mid-point of $CD$. Find the position vector of $D$. [2]

Accepted Answer

(i) l_AB: r = (5,4,10) + λ(3,0,4); (ii) 10 units; (iii) ON = (13/5, 4, 34/5); (iv) OD = (51/5, -1, 43/5)

N2000 P2 Q15 [Modified]

N2000 P2 Q15 [Modified]

Video Solution: