Let a-k- b-3-4-5k- If r-a-r-b and r-2-4-k-4- then the value of r-k-

Given :a=î ĵ+k̂, b=3î 4ĵ+5k̂. and nbsp;r×a=r×b nbsp; ⇒r×(a b)=0 So, r is parallel to vector (a b) ⇒r=λ(a b)=λ( 2î+3ĵ 4k̂) also, r·(2î+4ĵ+k̂)= 4 ⇒λ( 4+12 4)= ...

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Byju's Answer

Standard XII

Mathematics

Intersection of Sets

Let a=î-ĵ+k̂,...

Question

Let $\to a =^i -^j +^k, \to b = 3^i - 4^j + 5^k .$ If $\to r \times \to a = \to r \times \to b$ and $\to r \cdot (2^i + 4^j +^k) = - 4,$ then the value of $\to r \cdot (^i +^j +^k) =$

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Solution

Given : $\to a =^i -^j +^k, \to b = 3^i - 4^j + 5^k .$
and $\to r \times \to a = \to r \times \to b$
$\Rightarrow \to r \times (\to a - \to b) = 0$
So, $\to r$ is parallel to vector $(\to a - \to b)$
$\Rightarrow \to r = λ (\to a - \to b) = λ (- 2^i + 3^j - 4^k)$
also, $\to r \cdot (2^i + 4^j +^k) = - 4$
$\Rightarrow λ (- 4 + 12 - 4) = - 4 \Rightarrow λ = - 1 \Rightarrow \to r = 2^i - 3^j + 4^k$
$∴ \to r \cdot (^i +^j +^k) = 3$

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Intersection of Sets

Standard XII Mathematics

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Let →a=^i−^j+^k,→b=3^i−4^j+5^k. If →r×→a=→r×→b and →r⋅(2^i+4^j+^k)=−4, then the value of →r⋅(^i+^j+^k)=

Given :→a=^i−^j+^k,→b=3^i−4^j+5^k. and →r×→a=→r×→b ⇒→r×(→a−→b)=0 So, →r is parallel to vector (→a−→b) ⇒→r=λ(→a−→b)=λ(−2^i+3^j−4^k) also, →r⋅(2^i+4^j+^k)=−4 ⇒λ(−4+12−4)=−4⇒λ=−1⇒→r=2^i−3^j+4^k ∴→r⋅(^i+^j+^k)=3

Let $\to a =^i -^j +^k, \to b = 3^i - 4^j + 5^k .$ If $\to r \times \to a = \to r \times \to b$ and $\to r \cdot (2^i + 4^j +^k) = - 4,$ then the value of $\to r \cdot (^i +^j +^k) =$