If the vector a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle between b and c is 2 π 3 then |[a b c ]| = Options: A . &nbsp 24 B . &nbsp 12 C . &nbsp 12 √ 3 D . &nbsp 24 √ 3

Answer: Option C : C | [ a b c ] | = | a . ( b × c ) | = | a | | b × c | | c o s ( a , b × c ) | = | a | | b × c | = | a | | b | c | s i n ( b , c ) = 2.3.4 s i n ( 2 π 3 ) = 24. √ 3 2 = 12 √ 3 .

If the vector a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle

Discussion Forum : Vector Algebra

Question -

If the vector a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle between b and c is $\frac{2 π}{3}$ then |[a b c ]| =

Options:

A . 24

B . 12

C .

12 \sqrt{3}

D .

24 \sqrt{3}

Answer: Option C
:
C

| [a b c] | = | a . (b \times c) | = | a | | b \times c | | c o s (a, b \times c) | = | a | | b \times c | = | a | | b | c | s i n (b, c)

= 2.3.4 s i n (\frac{2 π}{3}) = 24. \frac{\sqrt{3}}{2} = 12 \sqrt{3}

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Discussion Forum : Vector Algebra

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