Find the value if - - - if the vectors a- 3-k- is perpendicular to the vector b- 2-k- and - a - - b -

The correct option is A 56 Here, #160; a · b = 0 6+λ μ = 0 #160; (i)and |a|=|b|⇒ 10+λ ^2= 5+μ ^2 or #160; #160; μ ^2 λ ^2= 5 ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Find the valu...

Question

Find the value if $λ$ + $μ$ , if the vectors $\to a = 3^i + λ^j -^k$ is perpendicular to the vector $\to b = 2^i +^j + μ^k$ and $| a | = | b |$

\frac{5}{6}

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Solution

The correct option is A $\frac{5}{6}$
Here, $a \cdot b = 0$
$6 + λ - μ = 0$ (i)
and $| a | = | b | \Rightarrow 10 + λ^{2} = 5 + μ^{2}$
or $μ^{2} - λ^{2} = 5$ or $(μ + λ) (μ - λ) = 5.$ .(ii)
Solving (i) and (ii) we get,

$λ = \frac{- 31}{12}, μ = \frac{41}{12}$
$λ$ + $μ$ $= \frac{5}{6}$

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Find the value if λ + μ, if the vectors →a=3^i+λ^j−^k is perpendicular to the vector →b=2^i+^j+μ^k and |a|=|b|

The correct option is A 56Here, a⋅b=06+λ−μ=0 (i)and |a|=|b|⇒10+λ2=5+μ2or μ2−λ2=5 or (μ+λ)(μ−λ)=5. .(ii)Solving (i) and (ii) we get,λ=−3112,μ=4112λ + μ =56

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