If a-i-j-k- b - i-j- c-i and a- b- c - - a- b- then - is equal to

The correct option is A 0 ( #10;a× b ) × c=( c . a #10; #160;) b ( c #10;. b #160;) a #10; #10; =λ a+μ b #10; #10; ...

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Multiplication with Vectors

If a=i+j+k,...

Question

If $a = i + j + k, b = i + j, c = i$ and $(a \times b) \times c = λ a + μ b$ , then $λ + μ$ is equal to

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Solution

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Similar questions

d = λ (a \times b) + μ (b \times c) + ν (c \times a)

[a b c] = \frac{1}{8}

λ + μ + ν

¯ ¯ ¯ d = λ (¯ ¯ ¯ a \times ¯ ¯ b) + μ (¯ ¯ b \times ¯ ¯ c) + δ (¯ ¯ c \times ¯ ¯ ¯ a)

[¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] = \frac{1}{8}

λ + μ + δ

a = a_{1} i + a_{2} j + a_{3} k, b = b_{1} i + b_{2} j + b_{3} k c = c_{1} i + c_{2} j + c_{3} k, | c | = 1

(a \times b) \times c = 0

{∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣}^{2}

\vec{a} \cdot \hat{i} = \vec{a} \cdot (\hat{i} + \hat{j}) = \vec{a} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1,

\vec{a} =

\vec{0}

\hat{i}

\hat{j}

\hat{i} + \hat{j} + \hat{k}

a = i - j + k, a \cdot b = 0, a \times b = c

c^{-} = - 2 i - j + k

b^{-}

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