Question 43 – 12.3 Solving Geometric Problems - Questions

Relative to a fixed origin $O$ :

the point $A$ has position vector $1i+2j−k1\mathbf{i} + 2\mathbf{j} - \mathbf{k}$
the point $B$ has position vector $3i−2j+7k3\mathbf{i} - 2\mathbf{j} + 7\mathbf{k}$

The line $l$ passes through $A$ and $B$ .

(i) Find $AB→\overrightarrow{AB}$ . (ii) Find a vector equation for the line $l$ .

The point $C$ has position vector $9i+0j+1k9\mathbf{i} + 0\mathbf{j} + 1\mathbf{k}$ . The point $P$ lies on $l$ . Given that $CP→\overrightarrow{CP}$ is perpendicular to $l$ :

Find the position vector of the point $P$ .

Relative to a fixed origin $O$ :

the point $A$ has position vector $1i+2j−k1\mathbf{i} + 2\mathbf{j} - \mathbf{k}$
the point $B$ has position vector $3i−2j+7k3\mathbf{i} - 2\mathbf{j} + 7\mathbf{k}$

The line $l$ passes through $A$ and $B$ .

(i) Find $AB→\overrightarrow{AB}$ . (ii) Find a vector equation for the line $l$ .

The point $C$ has position vector $9i+0j+1k9\mathbf{i} + 0\mathbf{j} + 1\mathbf{k}$ . The point $P$ lies on $l$ . Given that $CP→\overrightarrow{CP}$ is perpendicular to $l$ :

Find the position vector of the point $P$ .

12.3 Solving Geometric Problems

Question 34

12.3 Solving Geometric Problems

Question 34

12.3 Solving Geometric Problems

Question 34

12.3 Solving Geometric Problems Questions

12.3 Solving Geometric Problems

Question 34

12.3 Solving Geometric Problems Questions