If a-2 -3 -k- b-k- c-k- and let d- be such that a-b-d-b- d-c-8- then the value of d-b- is

(a d) ×b=0⇒a=d+λb nbsp; Taking dot product a of with c 2+3+1=8 + λ(1 1+1) ⇒λ= 2 d=a+2 b=4 î+ĵ+3 k̂ d·b=4 1+3=6 ...

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Cross Product of Two Vectors

If a⃗=2 î+3 ĵ...

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If $\to a = 2^i + 3^j +^k$ , $\to b =^i -^j +^k$ , $\to c =^i +^j +^k$ and let $\to d$ be such that $\to a \times \to b = \to d \times \to b, \to d \cdot \to c = 8$ , then the value of $\to d . \to b$ is

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\to a =^i +^j +^k, \to b =^i +^j -^k

\to c =^i -^j +^k

\to d =^i -^j -^k

(\to a \times \to b) \times (\to c \times \to d) =

\to a = 2^i +^j - 3^k, \to b =^i - 2^j +^k

\to c = -^i +^j - 4^k

\to d =^i +^j +^k

| (\to a \times \to b) \times (\to c \times \to d) |

\to a =^i +^j +^k

\to b =^i +^j -^k

\to c =^i -^j +^k

\to d =^i -^j -^k

| (\to a \times \to b) . (\to c \times \to d) | =

\to a =^i +^j +^k

\to b =^i -^j +^k

\to c =^i +^j -^k

\to a =^i -^j -^k

(\to a \times \to b) \times (\to c \times \to d)

\to a =^i -^j, \to b = \to j -^k, \to c =^k -^i . I f \to d

\to a . \to d = 0 = [\to b \to c \to d],

\to d

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