On a quiet day, Miss Loi sat in a lotus position in the Zen-like confines of The Temple to mark her students’ homework.
The gentle air-con breeze caressed her silky hair as, with a singular mind and soul that’s free from the worries of the world, she proceeded to ruthlessly splash red ink across those horrid lines of unintelligible workings.
A buzzing sound broke the Zen-like calm, as a fly settled on an opened page of the Vectors Chapter of her E-Maths textbook.
Down came Miss Loi’s 1000-Newton 如来神掌 (Explosive Buddha Palm???) upon the poor fly, to deliver swift justice for its trespassing.
Or so it seemed.
As someone who prides herself as a one-hit-one-kill ace, she watched in disbelief as the fly did a little flight of triumph before settling on another part of the Vectors page of the textbook.
Down came another 1000-Newton 如来神掌 … and another … and another, with the wily fly constantly able to avoid its fate at the last minute with each passing slam.
Nursing her swollen red palm, it suddenly dawned on her that, given The Temple‘s propensity to heighten the learning abilities of all living things in its proximity, the fly might have actually been reading and understanding the Vectors Chapter that it rested on, for it somehow managed to fly away with just the right speed (magnitude) and direction regardless of where Miss Loi’s lethal palm came hurling from.
But as a great leader once hypothesized, complacency can affect all of us. After the latest miss by Miss Loi, the fly was apparently finished with its Vectors page and settled instead on a piece of graph paper this time, taunting her with an arrogant glint on its eyes …
With the grids on the graph paper to guide her, Miss Loi pin-points the fly at position P. Recalling her mathematical powers, she calculated that she needs to place her palm at a starting position Q and slam the fly at point R.
- Write down an expression for
in terms of a and b. - Mark and label clearly on the grid the point Q such that
= a – b. The point R is such that
and = kb.- Mark and label clearly on the grid the point R.
- Find the value of h and k.
= kb.Note: Grids are labeled here to facilitate readers’ answers. They are normally unlabeled in actual exams as you’ll need to plot out the answers directly on the paper itself.
Can you help Miss Loi to 如来神掌 the fly into oblivion once and for all?
Vectors questions in your E-Maths exam can be broadly classified into two types:
- Those that end up asking you to mark on a grid diagram certain points that are expressed in terms of other vectors (like in the question of this blog post) or using the grid to find some column vector
![[matrix{2}{1}{a b}]](https://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_981_6cbeb753b174362408bfd59085c62e02.png "[matrix{2}{1}{a b}]")
. - Those that end up asking you to make use or calculate the ratios of two areas or lines like in this example, often requiring knowledge from other topics like similar triangles as well.
Regardless of the type of question, you’ll frequently end up using these basic vector properties:
8 Comments
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Usually when you see vector questions involving a grid like this one, expect to do some 'shifting'/'lengthening' of the vectors to form a couple of triangles (as shown in the ADDITION/SUBTRACTION OF VECTORS section of the notes above)
1. 3a-4b
Pretty straightforward to form the triangle consisting of 3 units of vector a and 4 units of b. Looking at the direction of the arrows, you can see that
3a =
+ 4b
= 3a - 4b
⇒
2. Q:(F,3)
Shifting a and b to form a triangle with a point at O (since we're finding
so one end has to be at O) we can then locate Q to be a (F, 3).
3i. R:(D,3)
ii. h=3, k=-1
Now,
which means that 
is parallel to 
(from the Scalar Multiple portion of the notes above). Furthermore, since there's a common point O this means that R must lie somewhere along grid-line #3.
So from this info, we can locate R at (D, 3) in the grid.
And looking at the diagram,
Care to share how you got k = -1 in your answer when
is in the SAME DIRECTION as b??? *scratch head*
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如 ... 来 ... 神 ... 掌!!! (in the direction of
)
*PIAAAAAAK*
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Good thing you pointed that out. It implies that
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Li-sa, umm ... your comment got truncated?
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erm....why such a title ? Dun sound good lei in this month... 🙂
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Cendrine: Thanks for your feedback 🙂
*Scraps title of next blog post: "Welcome To Hell"*
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Maybe "Li-sa" got k = -1 because she had somehow forgotten the question. Instead of subtracting
by 
she added 
to 
.
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.I: Perhaps. That's why it's always important to note the order of the letters in vectors e.g.
Speaking of which, Li-sa seems to have disappeared after leaving that mysterious truncated comment. Could she have been trapped in a recurrent time warp like what happened to Miss Loi awhile ago?