Let a=αi¯+j¯−k¯ and b=2i¯+j¯−αk¯,α>0. If the projection of a×b on the vector −i¯+2j¯−2k¯ is 30 then α =

c¯=−i¯+2j¯−2k¯a¯×b¯.c¯c¯=30[a¯ b¯ c¯]=30c¯α1−121−α−12−2=301+4+42α2−α−91=0⇒α=7,−132

Let a=αi¯+j¯−k¯ and b=2i¯+j¯−αk¯,α>0. If the projection of a×b on the vector −i¯+2j¯−2k¯ is 30 then α =

c¯=−i¯+2j¯−2k¯a¯×b¯.c¯c¯=30[a¯ b¯ c¯]=30c¯α1−121−α−12−2=301+4+42α2−α−91=0⇒α=7,−132

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Let $a = α \bar{i} + \bar{j} - \bar{k}$ and $b = 2 \bar{i} + \bar{j} - α \bar{k}, α > 0$ . If the projection of $a \times b$ on the vector $- \bar{i} + 2 \bar{j} - 2 \bar{k}$ is 30 then $α$ =

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$7$

$\frac{15}{2}$

$\frac{13}{2}$

answer is A.

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Detailed Solution

$\bar{c} = - \bar{i} + 2 \bar{j} - 2 \bar{k}$
$\begin{array}{l} \frac{\bar{a} \times \bar{b} . \bar{c}}{|\bar{c}|} = 30 \\ [\bar{a} \bar{b} \bar{c}] = 30 |\bar{c}| \\ |\begin{matrix} α & 1 & - 1 \\ 2 & 1 & - α \\ - 1 & 2 & - 2 \end{matrix}| = 30 \sqrt{1 + 4 + 4} \\ 2 α^{2} - α - 91 = 0 \Rightarrow α = 7, \frac{- 13}{2} \end{array}$