If | a | = 3 and | b | = 4 , then a value of for which a + b and a - b are perpendicular is:

Question

If $| \vec{a} |$ $= 3$ and $| \vec{b} |$ $= 4$ , then a value of $λ$ for which $\vec{a} + λ \vec{b}$ and $\vec{a} - λ \vec{b}$ are perpendicular is:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{3}{4}$

Explanation:

$\vec{a} + λ \vec{b}$ is perpendicular to $\vec{a} - λ \vec{b}$

So, $(\vec{a} + λ \vec{b}) \cdot (\vec{a} - λ \vec{b}) = 0$

$| \vec{a} |^{2}$ $- λ (\vec{a} \cdot \vec{b}) + λ (\vec{b} \cdot \vec{a}) - λ^{2}$ $| \vec{b} |^{2}$ $= 0$

$| \vec{a} |$ $= 3$

$| \vec{b} |$ $= 4$ $(Given)$

$| \vec{a} |^{2}$ $- λ^{2}$ $| \vec{b} |^{2}$ $= 0$

$3^{2} - λ^{2} 4^{2} = 0$

$λ^{2} = \frac{9}{16}$

$λ = \pm \frac{3}{4}$

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