Question Number 154948 by mathdanisur last updated on 23/Sep/21
$$\mathrm{If}\:\:\overset{\rightarrow} {\mathrm{a}}\:=\:\left(-\mathrm{1};\mathrm{0};-\mathrm{3};\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{b}}\:=\:\left(\mathrm{1};-\mathrm{4};\mathrm{0};-\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{c}}\:=\:\frac{\mid\overset{\rightarrow} {\mathrm{a}}\mid}{\mid\overset{\rightarrow} {\mathrm{b}}\mid}\:\centerdot\:\left(\mathrm{2}\overset{\rightarrow} {\mathrm{a}}\:+\:\overset{\rightarrow} {\mathrm{b}}\right) \\ $$$$\:\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{d}}\:=\:\frac{\mid\overset{\rightarrow} {\mathrm{b}}\mid}{\mid\overset{\rightarrow} {\mathrm{a}}\mid}\:\centerdot\:\left(\overset{\rightarrow} {\mathrm{a}}\:+\:\overset{\rightarrow} {\mathrm{b}}\right) \\ $$$$\:\:\:\:\:\:\:\overset{\rightarrow} {\mathrm{k}}\:=\:-\mathrm{3}\centerdot\left(\overset{\rightarrow} {\mathrm{c}}\:\centerdot\:\mid\overset{\rightarrow} {\mathrm{c}}\mid\:\centerdot\:\overset{\rightarrow} {\mathrm{d}}\right) \\ $$$$\mathrm{Find}\:\:\mid\overset{\rightarrow} {\mathrm{k}}\mid\:=\:? \\ $$
Commented by JDamian last updated on 23/Sep/21
how is defined the product of two vectors?
Commented by prakash jain last updated on 23/Sep/21
$$\overset{\rightarrow} {{c}}\centerdot\mid\overset{\rightarrow} {{c}}\mid\centerdot\overset{\rightarrow} {{d}}\:\mathrm{is}\:\mathrm{scaler}. \\ $$$$\mathrm{if}\:\centerdot\:\mathrm{is}\:\mathrm{dot}\:\mathrm{product} \\ $$
Commented by mathdanisur last updated on 23/Sep/21
$$\mathrm{Sorry}\:\boldsymbol{\mathrm{S}}\mathrm{er},\:\:\mid\overset{\rightarrow} {\mathrm{k}}\mid\:=\:-\mathrm{3}\left(\overset{\rightarrow} {\mathrm{c}}\:-\:\mid\overset{\rightarrow} {\mathrm{c}}\mid\:\centerdot\:\overset{\rightarrow} {\mathrm{d}}\right) \\ $$