Math  /  Geometry

Question13 Diberi segi tiga ABCA B C dengan ABundefined=4i6j\overrightarrow{A B}=4 \underset{\sim}{i}-6 \underset{\sim}{j} dan ACundefined=2i+4j.T\overrightarrow{A C}=2 \underset{\sim}{i}+4 \underset{\sim}{j} . T berada pada garis BCB C dengan keadaan 3BT=TC3 B T=T C. It is given that a triangle ABCA B C with ABundefined=4i6jACnd=2i+4j\overrightarrow{A B}=4 \underset{\sim}{i}-6 \underset{\sim}{j} \underset{\sim n d}{A C}=2 \underset{\sim}{i}+4 \underset{\sim}{j}. T lies on the line BCB C such that 3BT=TC3 B T=T C. (a) Cari vektor Find the vector (i) BCundefined\overrightarrow{B C}, (ii) ATundefined\overrightarrow{A T}. Seterusnya, car1 vektor unit dalam arah ATundefined\overrightarrow{A T}. ATundefined\overrightarrow{A T}. Hence, find the unit vector in the direction of ATundefined\overrightarrow{A T}. [5 markah] [5 marks] (b) Jika DD ialah satu titik dengan keadaan ADundefined=hBCundefined\overrightarrow{A D}=h \overrightarrow{B C} dan ADundefined=3i+kj\overrightarrow{A D}=-3 \underset{\sim}{i}+\underset{\sim}{k j}, dengan keadaan hh dan kk adalah pemalar. Cari nilai hh dan nilai kk. If DD is a point such that ADundefined=hBCundefined\overrightarrow{A D}=h \overrightarrow{B C} and ADundefined=3ii+k\overrightarrow{A D}=-3 i \underset{\sim}{i}+k, such that hh and kk are constants. Find the value of hh and of kk.

Studdy Solution
(a)(i) BCundefined=2i+10j\overrightarrow{BC} = -2\mathbf{i} + 10\mathbf{j} (a)(ii) ATundefined=72i72j\overrightarrow{AT} = \frac{7}{2}\mathbf{i} - \frac{7}{2}\mathbf{j}.
The unit vector is 12i12j\frac{1}{\sqrt{2}}\mathbf{i} - \frac{1}{\sqrt{2}}\mathbf{j}. (b) h=32h = \frac{3}{2} and k=15k = 15.

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