You visited us 6 times! Enjoying our articles? Unlock Full Access!

General Form of a Straight Line

The point of ...

Question

The point of intersection of the following lines is:
$l_{1} : r (t) = (i - 6 j + 2 k) + t (i + 2 j + k)$
$l_{2} : R (u) = (4 j + k) + u (2 i + j + 2 k)$

at the tip of

r (7)

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

at the tip of

R (4)

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

(8, 8, 9)

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

at the tip of

R (2)

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

Open in App

Solution

The correct options are
A $(8, 8, 9)$
B at the tip of $r (7)$
C at the tip of $R (4)$
$L_{1} = r (t) = (i - 6 j + 2 k) + t (i + 2 j + k)$
$L_{2} = R (u) = (4 j + k) + u (2 i + j + 2 k)$
$\Rightarrow r (7) = 8^i + 8^j + 9^k$
$\Rightarrow R (4) = 8^i + 8^j + 9^k$
Both the line intersect at the tip of $r (7)$ or $r (4)$
$ξ$ Clearly point of intersection is $(8, 8, 9)$ .
Hence, the answer is: at the tip of $r (7)$ , at the tip of $R (4)$ , $(8, 8, 9) .$

Suggest Corrections

Similar questions

L_{1} : \to r = \land 3 i - \land j + 2 \land k + λ (2 \land i + 4 \land j - \land k)

L_{2} : \to r = \land i - \land j + 3 \land k + μ (4 \land i + 2 \land j + 4 \land k)

L_{3} : \to r = \land 3 i + \land 2 j - 2 \land k + t (2 \land i + \land j + \land 2 k)

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

\vec{r} . (\hat{i} - 2 \hat{j} + \hat{k}) = 0

4 \hat{i} - \hat{j} - 3 \hat{k} and - 2 \hat{j} + \hat{j} - 2 \hat{k}

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

3 \hat{i} + 4 \hat{j} and \hat{i} + \hat{j} + \hat{k}

2 \hat{i} + 3 \hat{j} + 6 \hat{k} and 3 \hat{i} - 6 \hat{j} + 2 \hat{k}

a = (i + 2 j - k)

r . (3 i - j + k) = 1

r . (i + 4 j - 2 k) = 2.

\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