The point collinear with (1, -2, -3) and (2, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the given points be $A(1, -2, -3)$ and $B(2, 0, 0)$.The vector equation of the line passing through $A$ and $B$ is given by $\vec{r} = \vec{a}

Vedclass · Accepted Answer

$(0, -4, -6)$

Vedclass · Answer

(C) Let the given points be $A(1, -2, -3)$ and $B(2, 0, 0)$.The vector equation of the line passing through $A$ and $B$ is given by $\vec{r} = \vec{a} + t(\vec{b} - \vec{a})$, where $\vec{a} = \hat{i} - 2\hat{j} - 3\hat{k}$ and $\vec{b} = 2\hat{i}$.The direction vector is $\vec{v} = \vec{b} - \vec{a} = (2-1)\hat{i} + (0 - (-2))\hat{j} + (0 - (-3))\hat{k} = \hat{i} + 2\hat{j} + 3\hat{k}$.The line equation is $\vec{r} = (1\hat{i} - 2\hat{j} - 3\hat{k}) + t(\hat{i} + 2\hat{j} + 3\hat{k})$.This gives the parametric equations: $x = 1 + t$, $y = -2 + 2t$, $z = -3 + 3t$.For option $(C) (0, -4, -6)$, we set $x = 0 \implies 1 + t = 0 \implies t = -1$.Substituting $t = -1$ into $y$ and $z$: $y = -2 + 2(-1) = -4$ and $z = -3 + 3(-1) = -6$.Since the point $(0, -4, -6)$ satisfies the line equation, it is collinear.

The point collinear with $(1, -2, -3)$ and $(2, 0, 0)$ among the following is

Similar Questions

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is

$A$ particle moves in a circle of radius $25 \ cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

The tension $T$ in the string shown in the figure is:

$A$ ball of mass $2\;kg$ and another of mass $4\;kg$ are dropped together from a $60\;ft$ tall building. After a fall of $30\;ft$ each towards the Earth,their respective kinetic energies will be in the ratio of?

Vedclass Test Series

Exam Paper Generator

Online Exam Module