# Vectors Q (1 Viewer)

#### hmim

##### Member

Can someone show me their working for this question please, I'm a bit stuck

#### Average Boreduser

##### “If things go wrong, don’t go with them.”- Roger B
You can also use the cross product to solve this (though I'm not sure if its in the MX2 syllabus)
fr

#### tywebb

##### dangerman
You can also use the cross product to solve this (though I'm not sure if its in the MX2 syllabus)
Yeah it’s much shorter that way like

$\bg_white \lambda(\vec{i}-\vec{j}+2\vec{k})\times(2\vec{i}+\vec{j}-3\vec{k})=\lambda \begin{vmatrix}\vec{i}&\vec{j}&\vec{k}\\ 1&-1&2\\ 2&1&-3\end{vmatrix}=\lambda(\vec{i}+7\vec{j}+3\vec{k})\text{ for nonzero real numbers }\lambda$

but unfortunately that is not in the syllabus.

#### synthesisFR

##### Well-Known Member
Yeah it’s much shorter that way like

$\bg_white \lambda(\vec{i}-\vec{j}+2\vec{k})\times(2\vec{i}+\vec{j}-3\vec{k})=\lambda \begin{vmatrix}\vec{i}&\vec{j}&\vec{k}\\ 1&-1&2\\ 2&1&-3\end{vmatrix}=\lambda(\vec{i}+7\vec{j}+3\vec{k})\text{ for nonzero real numbers }\lambda$

but unfortunately that is not in the syllabus.
wat if i still use it in the HSC and impress markers

#### ExtremelyBoredUser

##### Bored Uni Student
You can also use the cross product to solve this (though I'm not sure if its in the MX2 syllabus)
Oh WOW look at this guy he's STUDIED MATH1141 and got a HIGH DISTINCTION He's so cool for bringing up the CROSS PRODUCT.

(inside joke iily temp no homo)

#### carrotsss

##### New Member
wat if i still use it in the HSC and impress markers
wat if u still use it in the HSC and get a 0 for the question because you got it wrong and used an out of syllabus technique

#### synthesisFR

##### Well-Known Member
wat if u still use it in the HSC and get a 0 for the question because you got it wrong and used an out of syllabus technique
suffering from success be like
imma find the marker and address this matter personally

#### tywebb

##### dangerman
wat if i still use it in the HSC and impress markers
I think it is going to be hard to penalise because some extension 2 texts use cross products despite it not being in the syllabus. They treat it as extension exercises. They don’t really go into it in much detail. Some IB texts have better and more thorough exercises on vectors including cross products, scalar triple products and their relation to coplanarity of vectors, minimum distance between skew lines using cross product and so on.

So exposure to this may mean some students will prefer to use quicker and more efficient methods in exams to save time, generally a good exam strategy.

The question posed in this thread however is a textbook question, not an exam question, so use of out-of-syllabus methods is OK.

If it were an exam question it might be more scaffolded to lead you into the longer method which I showed before.

#### =)(=

##### Active Member
bro cross product for this question is so overkill, if it was to find the equation of the plane then yea but for this its easier to sub a value for x and sovle from there

#### hmim

##### Member
Thank you so much guys. Yeah cross product is definitely much easier. I remember learning it back in year 10 IST