If x and y be two non-zero vectors such that - x-y - - x - and 2x- -y is perpendicular to y- then the value of - is

Given, | x+y |^2= | x |^2 ⇒ | y |^2+2x·y=0 ⋯ (i) and nbsp;(2x+λy)·y=0 ⇒λ| y|^2+2x·y=0 ⋯ (ii) by comparing (i) and (ii), we get we get λ=1 ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Vectors

If x and y be...

Question

If $\to x$ and $\to y$ be two non-zero vectors such that $∣ ∣ \to x + \to y ∣ ∣ = ∣ ∣ \to x ∣ ∣$ and $2 \to x + λ \to y$ is perpendicular to $\to y$ , then the value of $λ$ is

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Solution

Given, ${∣ ∣ \to x + \to y ∣ ∣}^{2} = {∣ ∣ \to x ∣ ∣}^{2}$
$\Rightarrow {∣ ∣ \to y ∣ ∣}^{2} + 2 \to x \cdot \to y = 0 \dots (i)$
and $(2 \to x + λ \to y) \cdot \to y = 0$
$\Rightarrow λ | \to y |^{2} + 2 \to x \cdot \to y = 0 \dots (i i)$
by comparing $(i)$ and $(i i),$ we get
we get $λ = 1$

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If →x and →y be two non-zero vectors such that ∣∣→x+→y∣∣=∣∣→x∣∣ and 2→x+λ→y is perpendicular to →y, then the value of λ is

Given, ∣∣→x+→y∣∣2=∣∣→x∣∣2 ⇒∣∣→y∣∣2+2→x⋅→y=0 ⋯(i) and (2→x+λ→y)⋅→y=0 ⇒λ|→y|2+2→x⋅→y=0 ⋯(ii) by comparing (i) and (ii), we get we get λ=1

If $\to x$ and $\to y$ be two non-zero vectors such that $∣ ∣ \to x + \to y ∣ ∣ = ∣ ∣ \to x ∣ ∣$ and $2 \to x + λ \to y$ is perpendicular to $\to y$ , then the value of $λ$ is