Maths A-Level Vectors

2. The points A, B and C have coordinates (-4, 0), (2, -1) and (3, 2) respectively.
(a) Write down the vectors
AB, AC and B. [3]
(b) Write down an equation linking vectors AB, AC and BC. [1]
(c) Find a unit vector in the direction of BC. [2]
(d) A fourth point D is positioned so that ABCD is a trapezium with AD parallel to BC and the magnitude of AD is 1.
Find the coordinates of D. [3]

How do you do part d?

(edited 8 months ago)

Reply 1

tonyiptony

11

Some formatting issues there, but I assume the question wants |AD| = 1 (reads "magnitude of AD is 1", or really it's just "length of AD is 1").

First off, did you draw diagram and find out where D is?
If so, a perhaps rather cryptic but still useful hint in spoilers:

Spoiler

(edited 8 months ago)

Reply 2

g3rnet333

OP

1

Original post by tonyiptony

Some formatting issues there, but I assume the question wants |AD| = 1 (reads "magnitude of AD is 1", or really it's just "length of AD is 1").

First off, did you draw diagram and find out where D is?
If so, a perhaps rather cryptic but still useful hint in spoilers:

Spoiler

I did draw a diagram but it did not seem to help, as I don't know the length of other vectors such as DC etc

Reply 3

tonyiptony

11

Original post by g3rnet333

I did draw a diagram but it did not seem to help, as I don't know the length of other vectors such as DC etc

You don't need the length of others.

So to find the positional vector of D from A, you only need 2 things:
(i) positional vector of A,
(ii) the vector AD (can you find this?).

Then do the tip-to-tail thing when adding vectors, right?. Or to write it more explicitly, vector OD = vector OA + vector AD (not the magnitude, just the vector).

(edited 8 months ago)

Reply 4

g3rnet333

OP

1

Original post by tonyiptony

You don't need the length of others.

So to find the positional vector of D from A, you only need 2 things:
(i) positional vector of A,
(ii) the vector AD (can you find this?).

Then do the tip-to-tail thing when adding vectors, right?. Or to write it more explicitly, vector OD = vector OA + vector AD (not the magnitude, just the vector).