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Condition That 2 Lines Are Coplanar

The value of ...

Question

The value of p for which the straight lines $\to r = (2^i + 9^j + 13^k) + t (^i + 2^j + 3^k)$ and $\to r = (- 3^i + 7^j + p^k) + s (-^i + 2^j - 3^k)$ are coplanar is

A

-1

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B

1

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C

-2

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D

2

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Solution

The correct option is C -2
$∣ ∣ ∣ ∣ \begin{matrix} 5 & 2 & 13 - p 1 & 2 & 3 - 1 & 2 & - 3 \end{matrix} ∣ ∣ ∣ ∣ = 0$ gives p = - 2

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Similar questions

Q. The value of p for which the straight lines

\to r = (2^i + 9^j + 13^k) + t (^i + 2^j + 3^k)

\to r = (- 3^i + 7^j + p^k) + s (-^i + 2^j - 3^k)

are coplanar is

Q. The value of p for which the straight lines

\to r = (2^i + 9^j + 13^k) + t (^i + 2^j + 3^k)

\to r = (- 3^i + 7^j + p^k) + s (-^i + 2^j - 3^k)

are coplanar is

Q. The vector equations of two lines

L_{1}

L_{2}

L_{2} : r = (2^i + 9^j + 13^k) + λ (^i + 2^j + 3^k)

L_{2} : r = (- 3^i + 7^j + p^k) + μ (-^i + 2^j - 3^k)

. Then, the lines

L_{1}

L_{2}

Q. The vector equation of the plane through the point

^i + 2^j -^k

and perpendicular to the line of intersection of the plane

¯ r . (3^i - 9^j +^k) = 1

¯ r . (^i + 4^j - 2^k) = 2

Q. For component of vector

\to P =^i + 2^j - 3^k

values are in column - II, then the correct match is:

\begin{matrix} Column I & Column II a) & X-axis & p) & 1 b) & Along vector & q) & \sqrt{14} \to q =^i + 2^j + \frac{5}{3}^k c) & Along vector & r) & 0 \to r = 2^i + 4^j - 6^k d) & Along vector & s) & \sqrt{7} \to s = \frac{^i + 2^j - 3^k}{\sqrt{14}} \end{matrix}

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