Let a-k-b- and c-2-3k- be three given vectors- lf r- is a vector such that r-b-c-b- and r-a-0- then the value of r-b- is

The correct option is C 9 Given r × b = c × b ⇒( r c ) × b = 0 So, r = c +λ b #160; #160; #160; #160; r =(1 λ )î +(2+ ...

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Byju's Answer

Standard XII

Mathematics

Dot Product of Two Vectors

Let a⃗=-î-k...

Question

Let $\to a = -^i -^k, \to b = -^i +^j$ and $\to c =^i + 2^j + 3^k$ be three given vectors. lf $\to r$ is a vector such that $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ , then the value of $\to r . \to b$ is

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Solution

The correct option is C $9$
Given $\to r \times \to b = \to c \times \to b$

$\Rightarrow (\to r - \to c) \times \to b = \to 0$

So, $\to r = \to c + λ \to b$

$\to r = (1 - λ)^i + (2 + λ)^j + 3^k$

$\to r . \to a = 0$

$\Rightarrow (1 - λ) (- 1) + 3 (- 1) = 0$

or, $λ = - 4$

$\Rightarrow \to r = - 3^i + 6^j + 3^k$

$\to r . \to b = (- 3) (- 1) + 6 (1) = 9$

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Let →a=−^i−^k,→b=−^i+^j and →c=^i+2^j+3^k be three given vectors. lf →r is a vector such that →r×→b=→c×→b and →r.→a=0, then the value of →r.→b is

The correct option is C 9Given →r×→b=→c×→b⇒(→r−→c)×→b=→0So, →r=→c+λ→b →r=(1−λ)^i+(2+λ)^j+3^k→r.→a=0⇒(1−λ)(−1)+3(−1)=0or, λ=−4⇒→r=−3^i+6^j+3^k→r.→b=(−3)(−1)+6(1)=9

Let $\to a = -^i -^k, \to b = -^i +^j$ and $\to c =^i + 2^j + 3^k$ be three given vectors. lf $\to r$ is a vector such that $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ , then the value of $\to r . \to b$ is