You are Here: Home

# C4 WJEC Vectors help?

Announcements Posted on
Did you have a flippin good pancake day, or was it pretty crepe? Share your pancake photos, videos and stories for a chance to win a £20 Amazon voucher! 05-03-2014
Offline
Reputation:
Hi there, I've been told vectors are easy but I really can't get my head around them Here's a question I'm trying to do from the 2007 paper:

9. (a) The position vectors of the points A and B, relative to a fixed origin O, are i + 3j – 2k and 3i + 6j + k, respectively.
(i) Find AB.
(ii) Find the vector equation of the line AB.
(iii) The vector equation of the line L is r = 2i + 3j + 7k + μ (i + j + 4k).
Given that L and AB intersect, find the position vector of the point of intersection.
(b) Find the angle between the vectors i + 2j – k and 3i – j + 2k.

for 9) i) am I right in thinking you have to use (i - 3i)^2 + (3j - 6j)^2 + (-2k - k)^2 and then take the square root of that? So 3j + 3k - 2?

For 9) ii) I think you have to use "r = a + tb". a and b here would be the lines i + 3j – 2k and 3i + 6j + k? What is t?

And as for the rest I have no idea. Thanks in advance
Offline
Reputation:
(Original post by Draco56)
Hi there, I've been told vectors are easy but I really can't get my head around them Here's a question I'm trying to do from the 2007 paper:

9. (a) The position vectors of the points A and B, relative to a fixed origin O, are i + 3j – 2k and 3i + 6j + k, respectively.
(i) Find AB.
(ii) Find the vector equation of the line AB.
(iii) The vector equation of the line L is r = 2i + 3j + 7k + μ (i + j + 4k).
Given that L and AB intersect, find the position vector of the point of intersection.
(b) Find the angle between the vectors i + 2j – k and 3i – j + 2k.

for 9) i) am I right in thinking you have to use (i - 3i)^2 + (3j - 6j)^2 + (-2k - k)^2 and then take the square root of that? So 3j + 3k - 2?
No, to find the direction vector, you just have to subtract OA from OB or the other way round.
For 9) ii) I think you have to use "r = a + tb". a and b here would be the lines i + 3j – 2k and 3i + 6j + k? What is t?
a could be either position vector of A or position vector of B. b is the direction vector of AB(which you're being asked in part (i)), and t is just a parameter.

And as for the rest I have no idea. Thanks in advance
Put vector equation of AB equal to vector equation of L, and find values of parameters μ and t by solving the simultaneous equations. Do you know the formula to find angle between two lines? The one which uses dot/scalar product?
Offline
Reputation:
Cheers! Gimme a minute and I'll see what answer I get.

Okay so:

a) i) 2i + 3j = 3k
ii) r = i + 3j - 2k + t(2i + 3j + 3k)
iii) -i - 5k
b) 96.3

Correct?
Offline
Reputation:
(Original post by Draco56)
Cheers! Gimme a minute and I'll see what answer I get.

Okay so:

a) i) 2i + 3j = 3k
ii) r = i + 3j - 2k + t(2i + 3j + 3k)
iii) -i - 5k
b) 96.3

Correct?
All are correct, except your answer to (b). Did you use ? That gives me an angle of 31.3 degrees.
Offline
Reputation:
(Original post by Zishi)
All are correct, except your answer to (b). Did you use ? That gives me an angle of 31.3 degrees.
I used that formula, but why AB and L? The question tells us to use i + 2j - k and 3i - j + 2k? Unless those are AB and L in this case and I did the calculations wrong. I did:

(1 x 3) + (2 x -1) + (2 x -1)
----------------------------------------------
sqrt(1^2 + 2^2 - 1^2)*sqrt(3^2 - 1^2 + 2^2)

Then took the inverse cos.
Offline
Reputation:
(Original post by Draco56)
I used that formula, but why AB and L? The question tells us to use i + 2j - k and 3i - j + 2k? Unless those are AB and L in this case and I did the calculations wrong. I did:

(1 x 3) + (2 x -1) + (2 x -1)
----------------------------------------------
sqrt(1^2 + 2^2 - 1^2)*sqrt(3^2 - 1^2 + 2^2)

Then took the inverse cos.
Ah, I didn't read the question again, so I thought that it was asking for the angle between AB and L. Anyway, you answer of 96.3 degrees is correct then.
Offline
Reputation:
Ah I see Thanks a lot for the help!

## Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty