The quadrilateral $$\(A B C D\)$$ is a trapezium in which $$\(A B\)$$ and $$\(D C\)$$ are parallel. With respect to the origin $$\(O\)$$, the position vectors of $$\(A, B\)$$ and $$\(C\)$$ are given by $$\(\overrightarrow{O A}=-\mathbf{i}+2 \mathbf{j}+3 \mathbf{k}, \overrightarrow{O B}=\mathbf{i}+3 \mathbf{j}+\mathbf{k}\)$$ and $$\(\overrightarrow{O C}=2 \mathbf{i}+2 \mathbf{j}-3 \mathbf{k}\)$$ Given that $$\(\overrightarrow{D C}=3 \overrightarrow{A B}\)$$, find the position vector of $$\(D\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No:9709_s21_qp_33 Year:2021 Question No:9(a)
Answer:
State or imply \(\overrightarrow{A B}=2 \mathbf{i}+\mathbf{j}-2 \mathbf{k}\)
Carry out a correct method to find \(\overrightarrow{O D}\)
Obtain answer \(-4 \mathbf{i}-\mathbf{j}+3 \mathbf{k}\)
Carry out a correct method to find \(\overrightarrow{O D}\)
Obtain answer \(-4 \mathbf{i}-\mathbf{j}+3 \mathbf{k}\)
Knowledge points:
3.7.2 carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms
3.7.3 calculate the magnitude of a vector, and use unit vectors, displacement vectors and position vectors (In 2 or 3 dimensions.)
Solution:
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