TS EAMCET · Maths · Vector Algebra
Three non-coplanar vectors \(\bar{a}, \bar{b}, \bar{c}\) are the coterminous edges of a parallelepiped. If \(\bar{a}\) and \(\bar{b}\) determine the base of the parallelepiped then its height is
- A \(\frac{|[\bar{a} \bar{b} \bar{c}]|}{|\bar{b} \times \bar{c}|}\)
- B \(\frac{|[\bar{a} \bar{b} \bar{c}]|}{|\bar{a} \times \bar{b}|}\)
- C \(\frac{|[\bar{a} \bar{b} \bar{c}]|}{|\bar{a} \times \bar{c}|}\)
- D \(\frac{|[\bar{a} \bar{b} \bar{c}]|}{|\bar{b}+\bar{c}|}\)
Answer & Solution
Correct Answer
(B) \(\frac{|[\bar{a} \bar{b} \bar{c}]|}{|\bar{a} \times \bar{b}|}\)
Step-by-step Solution
Detailed explanation
We know that volume of parallelopiped is \(\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]\). \(\therefore\) Height is parallel to the normal vector to the base.…
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