Question

If $\overset{\rightarrow}{a}$= (5$\overset{\hat{}}{i}$ – $\overset{\hat{}}{j}$ + $\overset{\hat{}}{k}$); $\overset{\rightarrow}{b}$= 2$\overset{\hat{}}{i}$ – 3$\overset{\hat{}}{j}$ – $\overset{\hat{}}{k}$;$\overset{\rightarrow}{c}$ =–3$\overset{\hat{}}{i}$ + $\overset{\hat{}}{j}$ + $\overset{\hat{}}{k}$ and $\overset{\rightarrow}{d}$= 2$\overset{\hat{}}{j}$ + $\overset{\hat{}}{k}$, then the value of $\overset{\rightarrow}{d}$ [$\overset{\rightarrow}{a}$×{b($\overset{\rightarrow}{c}$×$\overset{\rightarrow}{d}$)}] is equal to

• A. 100
• B. 99
• C. 98
• D. 96

Answer 1

Answer: (C)

98

Answer 2

E º $\overset{\rightarrow}{d}$. [$\overset{\rightarrow}{a}$× ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{c}$×$\overset{\rightarrow}{d}$)]

=$\overset{\rightarrow}{d}$ [$\overset{\rightarrow}{a}$× ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{d}$)$\overset{\rightarrow}{c}$– ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{d}$)$\overset{\rightarrow}{d}$

=$\overset{\rightarrow}{d}$×[($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{d}$) ($\overset{\rightarrow}{a}$×$\overset{\rightarrow}{c}$) – ($\overset{\rightarrow}{a}$×$\overset{\rightarrow}{d}$) ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{c}$)]

E º ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{a}$) [$\overset{\rightarrow}{d}$ $\overrightarrow { \mathrm { a } }$ $\overset{\rightarrow}{c}$]– ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{c}$)

[$\overset{\rightarrow}{d}$×($\overset{\rightarrow}{a}$×$\overset{\rightarrow}{d}$)]/2

= ($\overset{\rightarrow}{b}$×$\overset{\rightarrow}{d}$) [$\overset{\rightarrow}{d}$ $\overrightarrow { \mathrm { a } }$ $\overset{\rightarrow}{c}$]

Putting values, we get E = 98