1. ## coordinate system

Hey All,

How would you solve the following vector question:

In a cartestian coordinate system, point A is given by (-3, 0, -5) and a point B by (3, 4, 3). Find the direction cosines of the line AB and write down the vector equation for this line.

A second line passes through point C with coordinates (2, 5, 5), and is in the direction (2i + 3j + 6k). show that these two lines intersect at a point D and write down the coordinate of D.

Find a vector that is perpendicular to both AB and CD.

Thank you

Hey All,

How would you solve the following vector question:

In a cartestian coordinate system, point A is given by (-3, 0, -5) and a point B by (3, 4, 3). Find the direction cosines of the line AB and write down the vector equation for this line.

A second line passes through point C with coordinates (2, 5, 5), and is in the direction (2i + 3j + 6k). show that these two lines intersect at a point D and write down the coordinate of D.

Find a vector that is perpendicular to both AB and CD.

Thank you
Vector equation of AB

r = point on AB + t(direction of AB)

r = (-3i - 5k) + t(6i + 4j + 8k)

[Direction of AB = position vector of point B - position vector of point A]

Second line has vector equation

s = (2i + 5j + 5k) + u(2i + 3j + 6k)

Make two vector equations equal to each other and equate coefficients

(-3i - 5k) + t(6i + 4j + 8k) = (2i + 5j + 5k) + u(2i + 3j + 6k)

giving

for i

-3 + 6t = 2 + 2u

for j

4t = 5 + 3u

for k

-5 + 8t = 5 + 6u

Take two of these three equations and solve simultaneously to find t and u

Stick the found values of t and u into the third equation

If they work the lines intersect, if they don't the lines don't intersect

Stick either your value of t into r = (-3i - 5k) + t(6i + 4j + 8k) or your value of u into s = (2i + 5j + 5k) + u(2i + 3j + 6k) to find D

3. Originally Posted by Glaysher
r = (-3i - 5k) + t(6i + 4j + 8k)
Hi,

How do you get (-3i -5k)

are you using the dot or cross product rule?

Thanks

Hi,

How do you get (-3i -5k)

are you using the dot or cross product rule?

Thanks
Neither, (-3i -5k) reprsents position vector of point A (-3, 0, -5)

Hey All,

How would you solve the following vector question:

In a cartestian coordinate system, point A is given by (-3, 0, -5) and a point B by (3, 4, 3). Find the direction cosines of the line AB and write down the vector equation for this line.

A second line passes through point C with coordinates (2, 5, 5), and is in the direction (2i + 3j + 6k). show that these two lines intersect at a point D and write down the coordinate of D.

Find a vector that is perpendicular to both AB and CD.

Thank you
Cross product of (6i + 4j + 8k) and (2i + 3j + 6k) gives vector perpendicular to AB and CD

6. Thank you