Question

If , , $\overrightarrow { \mathrm { c } }$ represents adjacent edges of parallelopiped then its volume is-

• A. $\frac { 2 \sqrt { 2 } } { \sqrt { 3 } }$
• B. $\frac { 2 \sqrt { 2 } } { 3 }$
• C. 4 $\sqrt { 2 }$
• D. $\sqrt { \frac { 2 } { 3 } }$

Answer 1

Answer: (C)

4 $\sqrt { 2 }$

Answer 2

Let $\overrightarrow { \mathrm { c } }$ = l (+ ) + m (+)

taking dot product with , we get

2 = l [4 + 2] Ž l = $\frac { 1 } { 3 }$

squaring 4 = l²[4 + 4 + 4] = m². 12

Ž m² = $\frac { 2 } { 9 }$

Ž taking dot product with (× )

[(× ). $\overrightarrow { \mathrm { c } }$ ] = m (12)

= $\frac { \sqrt { 2 } } { 3 }$ × 12 = 4$\sqrt { 2 }$