Let a¯=3i¯+2j¯+2k¯ and b¯=i¯+2j¯−2k¯ be vectors. If a vector perpendicular to both the vector a¯+b¯ and a¯−b¯ has the magnitude 12 then one such vector is

(a¯+b¯)×(a¯−b¯)=2(b¯×a¯)=2(8i¯−8j¯−4k¯)Rev vector =±12.(2i¯−2j¯−k¯)3=±4(2i¯−2j¯−k¯)

Let a¯=3i¯+2j¯+2k¯ and b¯=i¯+2j¯−2k¯ be vectors. If a vector perpendicular to both the vector a¯+b¯ and a¯−b¯ has the magnitude 12 then one such vector is

(a¯+b¯)×(a¯−b¯)=2(b¯×a¯)=2(8i¯−8j¯−4k¯)Rev vector =±12.(2i¯−2j¯−k¯)3=±4(2i¯−2j¯−k¯)

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Let $\bar{a} = 3 \bar{i} + 2 \bar{j} + 2 \bar{k}$ and $\bar{b} = \bar{i} + 2 \bar{j} - 2 \bar{k}$ be vectors. If a vector perpendicular to both the vector $\bar{a} + \bar{b}$ and $\bar{a} - \bar{b}$ has the magnitude 12 then one such vector is

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$4 (2 \bar{i} + 2 \bar{j} + 3 \bar{k})$

$4 (- 2 \bar{i} - 3 \bar{j} + \bar{k})$

$4 (2 \bar{i} - 2 \bar{j} - \bar{k})$

$4 (3 \bar{i} + 2 \bar{j} - \bar{k})$

answer is C.

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$(\bar{a} + \bar{b}) \times (\bar{a} - \bar{b}) = 2 (\bar{b} \times \bar{a}) = 2 (8 \bar{i} - 8 \bar{j} - 4 \bar{k})$
Rev vector $= \pm 12. \frac{(2 \bar{i} - 2 \bar{j} - \bar{k})}{3} = \pm 4 (2 \bar{i} - 2 \bar{j} - \bar{k})$

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Let a¯=3i¯+2j¯+2k¯ and b¯=i¯+2j¯−2k¯ be vectors. If a vector perpendicular to both the vector a¯+b¯ and a¯−b¯ has the magnitude 12 then one such vector is

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Let $\bar{a} = 3 \bar{i} + 2 \bar{j} + 2 \bar{k}$ and $\bar{b} = \bar{i} + 2 \bar{j} - 2 \bar{k}$ be vectors. If a vector perpendicular to both the vector $\bar{a} + \bar{b}$ and $\bar{a} - \bar{b}$ has the magnitude 12 then one such vector is