If a¯=3i¯-5j¯, b¯=6i¯+3j¯ are two vectors and c¯ is a vector such that c¯=a¯Xb¯, then a¯:b¯:c¯=

a×b=ijk3-50630=i(0-0)-j(0-0)+k(9+30) |a|=9+25=34 |b|=36+9=458 |c|=(39)2=39 |a| : |b| : |c|=34 : 45 : 39

If a¯=3i¯-5j¯, b¯=6i¯+3j¯ are two vectors and c¯ is a vector such that c¯=a¯Xb¯, then a¯:b¯:c¯=

a×b=ijk3-50630=i(0-0)-j(0-0)+k(9+30) |a|=9+25=34 |b|=36+9=458 |c|=(39)2=39 |a| : |b| : |c|=34 : 45 : 39

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$If \bar{a} = 3 \bar{i} - 5 \bar{j}, \bar{b} = 6 \bar{i} + 3 \bar{j} are two vectors and \bar{c} is a vector such that \bar{c} = \bar{a} X \bar{b}, then |\bar{a}| : |\bar{b}| : |\bar{c}| =$

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$\sqrt{34} : \sqrt{45} : \sqrt{39}$

$34 : 39 : 45$

$39 : 35 : 34$

$\sqrt{34} : \sqrt{45} : 39$

answer is B.

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Detailed Solution

$a \times b = |\begin{matrix} i & j & k \\ 3 & - 5 & 0 \\ 6 & 3 & 0 \end{matrix}| = i (0 - 0) - j (0 - 0) + k (9 + 30) | a | = \sqrt{9 + 25} = \sqrt{34} | b | = \sqrt{36 + 9} = \sqrt{458} | c | = \sqrt{{(39)}^{2}} = 39 | a | : | b | : | c | = \sqrt{34} : \sqrt{45} : 39$