You visited us 1 times! Enjoying our articles? Unlock Full Access!

Condition for Coplanarity of Four Points

Equation of t...

Question

Equation of the plane containing the lines $¯ ¯ ¯ r = (¯ i - 2 ¯ j + ¯ ¯ ¯ k) + t (¯ i + 2 ¯ j - ¯ ¯ ¯ k)$ , $¯ ¯ ¯ r = (¯ i + 2 ¯ j - ¯ ¯ ¯ k) + s (¯ i + ¯ j + 3 ¯ ¯ ¯ k)$ is

¯ ¯ ¯ r (7 ¯ i - 4 ¯ j - ¯ ¯ ¯ k) = 14

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

¯ ¯ ¯ r (¯ i + 2 ¯ j - ¯ ¯ ¯ k) = 10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

¯ ¯ ¯ r (¯ i + ¯ j + 3 ¯ ¯ ¯ k) = 20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

¯ ¯ ¯ r (¯ i - 2 ¯ j + ¯ ¯ ¯ k) = 27

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $¯ ¯ ¯ r (7 ¯ i - 4 ¯ j - ¯ ¯ ¯ k) = 14$
The parallel vectors in plane $(^i + 2^j +^k), (^i +^j + 3^k)$
$\to n = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & 2 & - 1 1 & 1 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 7^i - 4^j -^k$

$\to r . \to n = (^i - 2^j +^k) (7^i - 4^j -^k)$
$\to r . (7^i - 4^j -^k) = 14$

Suggest Corrections

Similar questions

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

¯ ¯ ¯ r (¯ i + 5 ¯ j + ¯ ¯ ¯ k) = 5

\vec{r} = \hat{i} - \hat{j} + λ (\hat{i} + \hat{j} + \hat{k}) + μ (\hat{i} - 2 \hat{j} + 3 \hat{k})

\vec{r} \cdot (5 \hat{i} - 2 \hat{j} - 3 \hat{k}) = 7

\vec{r} \cdot (5 \hat{i} + 2 \hat{j} - 3 \hat{k}) = 7

\vec{r} \cdot (5 \hat{i} - 2 \hat{j} + 3 \hat{k}) = 7

[(3 i - 2 j - 2 k) \times (i - k)] \times [(i + j + k) \times (i - 2 j + 3 k)]

\vec{r} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}) and \vec{r} = (2 \hat{i} - \hat{j} - \hat{k}) + μ (- \hat{i} + \hat{j} - \hat{k})

\vec{r} = (\hat{i} + \hat{j}) + λ (2 \hat{i} - \hat{j} + \hat{k}) and \vec{r} = (2 \hat{i} + \hat{j} - \hat{k}) + μ (4 \hat{i} - 2 \hat{j} + 2 \hat{k})

\vec{r} = 3 \hat{i} + 8 \hat{j} + 3 \hat{k} + λ (3 \hat{i} - \hat{j} + \hat{k}) and \vec{r} = - 3 \hat{i} - 7 \hat{j} + 6 \hat{k} + μ (- 3 \hat{i} + 2 \hat{j} + 4 \hat{k})

\vec{r} = (3 \hat{i} + 5 \hat{j} + 7 \hat{k}) + λ (\hat{i} - 2 \hat{j} + 7 \hat{k}) and \vec{r} = - \hat{i} - \hat{j} - \hat{k} + μ (7 \hat{i} - 6 \hat{j} + \hat{k})

\vec{r} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) and \vec{r} = (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + μ (3 \hat{i} + 4 \hat{j} + 5 \hat{k})

\vec{r} = (1 - t) \hat{i} + (t - 2) \hat{j} + (3 - t) \hat{k} and \vec{r} = (s + 1) \hat{i} + (2 s - 1) \hat{j} - (2 s + 1) \hat{k}

\vec{r} = (λ - 1) \hat{i} + (λ + 1) \hat{j} - (1 + λ) \hat{k} and \vec{r} = (1 - μ) \hat{i} + (2 μ - 1) \hat{j} + (μ + 2) \hat{k}

\vec{r} = (2 \hat{i} - \hat{j} - \hat{k}) + λ (2 \hat{i} - 5 \hat{j} + 2 \hat{k}) and, \vec{r} = (\hat{i} + 2 \hat{j} + \hat{k}) + μ (\hat{i} - \hat{j} + \hat{k})

\vec{r} = (\hat{i} + \hat{j}) + λ (2 \hat{i} - \hat{j} + \hat{k}) and, \vec{r} = 2 \hat{i} + \hat{j} - \hat{k} + μ (3 \hat{i} - 5 \hat{j} + 2 \hat{k})

\vec{r} = (8 + 3 λ) \hat{i} - (9 + 16 λ) \hat{j} + (10 + 7 λ) \hat{k}

\vec{r} = 15 \hat{i} + 29 \hat{j} + 5 \hat{k} + μ (3 \hat{i} + 8 \hat{j} - 5 \hat{k})

Join BYJU'S Learning Program