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Question Number 132257 by Salman_Abir last updated on 12/Feb/21

Answered by bemath last updated on 12/Feb/21

$$\left(\mathrm{i}\right)\mathrm{E}(0,0,8),\mathrm{C}(3,3,0)\mathrm{vector}$$$$\mathrm{EC}=3\hat{\mathrm{i}}+3\hat{\mathrm{j}}-8\hat{\mathrm{k}};\mid \mathrm{EC}\mid =\sqrt{9+9+64}=\sqrt{82}$$$$\mathrm{H}(0,3,8),\mathrm{B}(3,0,0)\mathrm{vector}$$$$\mathrm{HB}=3\hat{\mathrm{i}}-3\hat{\mathrm{j}}-8\hat{\mathrm{k}};\mid \mathrm{HB}\mid =\sqrt{82}$$$$\mathrm{so}\mid \mathrm{EC}\mid =\mid \mathrm{HB}\mid \mathrm{but}\mathrm{EC}\ne \mathrm{HB}$$$$\left(\mathrm{ii}\right)\mathrm{vector}\mathrm{HG}=\{\begin{array}{l}\mathrm{EF};\mathrm{AB}\\ \mathrm{DC}\end{array}$$$$\left(\mathrm{iii}\right)\mathrm{EF}+\mathrm{BD}+\mathrm{CF}=\mathrm{AB}+\mathrm{BD}+\mathrm{CF}=\mathrm{BF}$$

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