Let a-2-k- and b-k- be two vectors- If c is a vector such that b-c-b-a and c-a-0- then c-b is equal to -

A=î 2ĵ+k̂ b=î ĵ+k̂ b×c=b×a ⇒a× (b×c)=a× (b×a) ⇒ (a·c)b (a·b) c=(a·a)b (a·b)a ⇒ (a·b) c=(a·a) b (a·b) a ⇒ 4c=6(î ĵ+k̂) 4(î 2ĵ+k̂) ⇒c= 12(î+ĵ+k̂) ∴b·c= 12 ...

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Byju's Answer

Standard XII

Mathematics

Vector Triple Product

Let a=î-2ĵ+k̂...

Question

Let $\to a =^i - 2^j +^k$ and $\to b =^i -^j +^k$ be two vectors. If $\to c$ is a vector such that $\to b \times \to c = \to b \times \to a$ and $\to c \cdot \to a = 0$ , then $\to c \cdot \to b$ is equal to :

\frac{1}{2}

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- \frac{3}{2}

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- \frac{1}{2}

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Solution

The correct option is C $- \frac{1}{2}$
$\to a =^i - 2^j +^k$
$\to b =^i -^j +^k$
$\to b \times \to c = \to b \times \to a$
$\Rightarrow \to a \times (\to b \times \to c) = \to a \times (\to b \times \to a)$
$\Rightarrow (\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c = (\to a \cdot \to a) \to b - (\to a \cdot \to b) \to a$
$\Rightarrow - (\to a \cdot \to b) \to c = (\to a \cdot \to a) \to b - (\to a \cdot \to b) \to a$
$\Rightarrow - 4 \to c = 6 (^i -^j +^k) - 4 (^i - 2^j +^k)$
$\Rightarrow \to c = - \frac{1}{2} (^i +^j +^k)$
$∴ \to b \cdot \to c = - \frac{1}{2}$

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Let →a=^i−2^j+^k and →b=^i−^j+^k be two vectors. If →c is a vector such that →b×→c=→b×→a and →c⋅→a=0, then →c⋅→b is equal to :

Let $\to a =^i - 2^j +^k$ and $\to b =^i -^j +^k$ be two vectors. If $\to c$ is a vector such that $\to b \times \to c = \to b \times \to a$ and $\to c \cdot \to a = 0$ , then $\to c \cdot \to b$ is equal to :