Find the value of - so that the vector A -2- - -k- - B -4- -2- -2k- are perpendicular to each other

A . B =( 2× 4 ) ( λ×( 2 ) #160; ) +( 1×( 2 ) #160; ) =8+2λ +2=0 ⇒ 10=2λ ⇒λ =5 ...

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Multiplication with Vectors

Find the valu...

Question

Find the value of $λ$ so that the vector $¯ ¯¯ ¯ A = 2^i + λ^j -^k, ¯ ¯¯ ¯ B = 4^i - 2^j - 2^k$ are perpendicular to each other

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Solution

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¯ ¯ ¯ r = (4^i -^j) + λ (^i + 2^j - 3^k)

¯ ¯ ¯ r = (^i -^n j + 2^k) + μ (^i + 4^j - 5^k)

λ

μ

λ

(λ^i +^j -^k) \times (3^i - 2^j + 4^k) = (2^i - 11^j - 7^k)

{\to V}_{1} =^i +^j - 2^k, {\to V}_{2} =^i - 2^j +^k, {\to V}_{3} = - 2^i + 2^j +^k

\to V

{\to V}_{1}

{\to V}_{2}

\to V {\to V}_{3} = 0

\to V

^i -^j +^k

6 \sqrt{3}

\to V = λ (^i + 3^j - 4^k)

λ

\to a =^i +^j +^k, \to b = 2^i - 4^k, \to c =^i + λ^j + 3^k

λ

\to a = 2^i +^j +^k, \to b = 3^i - 4^j + 2^k, \to c =^i - 2^j + 2^k

\to a + \to b

\to c

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