Question Number 134428 by liberty last updated on 03/Mar/21
![In a cube ABCD.EFGH with a side length of 4 cm. Point Q is the middle of line AE and point P lies on the extension of line AB so that BP : AB = 1 : 2. If θ is the angle between the QG line and the PQH plane , then sin θ =?](https://www.tinkutara.com/question/Q134428.png)
$$\mathrm{In}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{4}\:\mathrm{cm}.\:\mathrm{Point}\:\mathrm{Q}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{middle}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AE}\:\mathrm{and}\:\mathrm{point}\:\mathrm{P} \\ $$$$\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{extension}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AB} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{BP}\::\:\mathrm{AB}\:=\:\mathrm{1}\::\:\mathrm{2}.\:\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\:\mathrm{QG}\:\mathrm{line}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{PQH}\:\mathrm{plane}\:,\:\mathrm{then}\:\mathrm{sin}\:\theta\:=?\: \\ $$
Answered by EDWIN88 last updated on 03/Mar/21
![let Q(4,0,2) , P(4,6,0) and H(0,0,4) n^→ = QH × QP = determinant (((−4 0 2)),(( 0 6 −2)))= −12i^](https://www.tinkutara.com/question/Q134429.png)