If the coordinates of the points P, Q, R, S a | vedclass

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

Question

(D) The direction ratios of line $PQ$ are $(4-1, 5-2, 7-3) = (3, 3, 4)$.The direction ratios of line $RS$ are $(2-(-4), 0-3, 2-(-6)) = (6, -3, 8)$.For

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The direction ratios of line $PQ$ are $(4-1, 5-2, 7-3) = (3, 3, 4)$.The direction ratios of line $RS$ are $(2-(-4), 0-3, 2-(-6)) = (6, -3, 8)$.For $PQ \parallel RS$,the ratios of direction ratios must be equal: $\frac{3}{6} = \frac{3}{-3} = \frac{4}{8}$,which is $\frac{1}{2} = -1 = \frac{1}{2}$. This is false.For $PQ \perp RS$,the dot product of direction ratios must be zero: $(3)(6) + (3)(-3) + (4)(8) = 18 - 9 + 32 = 41 
eq 0$. This is false.For $PQ = RS$,the lengths are $PQ = \sqrt{3^2 + 3^2 + 4^2} = \sqrt{9 + 9 + 16} = \sqrt{34}$ and $RS = \sqrt{6^2 + (-3)^2 + 8^2} = \sqrt{36 + 9 + 64} = \sqrt{109}$. Since $\sqrt{34} 
eq \sqrt{109}$,this is false.Therefore,none of the given options are correct.

If the coordinates of the points $P, Q, R, S$ are $(1, 2, 3), (4, 5, 7), (-4, 3, -6)$ and $(2, 0, 2)$ respectively,then:

Similar Questions

If $\theta$ is the acute angle between the two lines whose direction cosines are connected by the relations $l+m+n=0$ and $2lm+2nl-mn=0$, then $\cos \theta=$

If the direction ratios of two lines are given by $a+2b+c=0$ and $11bc+6ca-14ab=0$, then the angle between these lines is

If the projections of a line segment on the coordinate axes are $3, 4,$ and $5$,then its length is:

If a line makes an angle of $\pi /4$ with the positive direction of both the $x$-axis and $y$-axis,what angle does it make with the positive direction of the $z$-axis?

$A$ ray makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$ and $Z$-axes respectively. Then,the value of the sine of the angle made by the ray with $X$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module