Question

$\overset{\rightarrow}{a}=\beta i+2j +2k , \overset{\rightarrow}{b} = 2i + 2j + \beta k$ എന്നീ സദിശങ്ങൾ ലംബങ്ങളായാൽ $|\overset{\rightarrow}{a}+\overset{\rightarrow}{b}|-|\overset{\rightarrow}{a}-\overset{\rightarrow}{b}|=$

• A. 2
• B. 1
• C. 0
• D. -1

Answer 1

Answer:

C. 0

\overset{\rightarrow}{a} , \overset{\rightarrow}{b} ലംബങ്ങളായാൽ $\overset{\rightarrow}{a}.\overset{\rightarrow}{b}=0$

$2\beta + 4 + 2\beta = 0$

$4\beta = -4$

$\beta=-1$

$\overset{\rightarrow}{a}=-i+2j+2k ; \overset{\rightarrow}{b}=2i+2j-k$

$\overset{\rightarrow}{a}+\overset{\rightarrow}{b}=i+4j+k$

$\overset{\rightarrow}{a}-\overset{\rightarrow}{b}=-3i+0j+3k$

$|\overset{\rightarrow}{a}+\overset{\rightarrow}{b}|-|\overset{\rightarrow}{a}-\overset{\rightarrow}{b}|= \sqrt{1+16+1}-\sqrt{9+9}$

$=0$