The vector equation of the line through the point $A (3, 4, - 7)$ and $B (1, - 1, 6)$ is which of the following?

\to r = (3^i + 4^j - 7^k) + λ (^i -^j + 6^k)

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\to r = (^i +^j + 6^k) + λ (3^i - 4^j + 7^k)

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\to r = 3^i + 4^j - 7^k + λ (- 2^i - 5^j + 13^k)

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None of these

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Solution

The correct option is A $\to r = (3^i + 4^j - 7^k) + λ (^i -^j + 6^k)$
$A (3, 4, - 7) a n d B (1, - 1, 6) - - \to A B = - - \to O A + λ (\to B - \to A) - - \to A B = 3^i + 4^j - 7^k + λ (- 2^i - 5^j + 13^k)$

Suggest Corrections

Similar questions

\to r = 2^i - 5^j +^k + λ (3^i - 2^j + 6^k)

\to r = 7^i - 6^k + μ (^i + 2^j + 2^k)

\to r = 3^i +^j - 2^k + λ (^i -^j - 2^k)

\to r = 2^i -^j - 56^k + μ (^3 i - 5^j - 4^k)

\to r = 3^i + 5^j + 7^k + λ (^i + 2^j +^k) a n d \to r = -^i -^j -^k + μ (7^i - 6^j +^k) i s

If a displacement vector of $A B$ is $^i +^j + 2^k$ and point $A$ having a position vector $2^i + 5^j + 6^k$ , then find the position vector of $B$ ?

\to r = 3^i + 8^j + 3^k + λ (3^i -^j +^k)

\to r = - 3^i - 7^j + 6^k + μ (- 3^i + 2^j + 4^k)

\to r = 3^i +^j - 2^k + λ (^i +^j - 2^k)

\to r = 2^i -^j - 56^k + μ (3^i - 5^j - 4^k)

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