lf AB then the value of equal, where A(2k, 2, 3), B(k, 1, 5), C(3… - Vidyadip

MCQ

lf $\text{AB}\perp\text{BC}$ then the value of $\lambda$ equal, where $A(2k, 2, 3), B(k, 1, 5), C(3 + k, 2, 1):$

A
$3$
B
$\frac{1}{3}$
✓
$-3$
D
$-\frac{1}{3}$

✓

Answer

Correct option: C.

$-3$

The drs of $AB$ are $(k, 1, -2)$
The drs of $BC$ are $(3, 1, -4)$
Since, they are perpendicular, $\text{AB.BC} = 0$
$3k + 1 + 8 = 0$
$k = -3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\vec{\text{a}}$ and $\vec{\text{b}}$ be two unit vectors and a be the angle between them. Then, $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if:

Let the function, $f:[-7,0] \rightarrow R$ be continuous on $[-7,0]$ and differentiable on $(-7,0)$ If $f(-7)=-3$ and $f(x) \leq 2,$ for all $x \in(-7,0),$ then for all such functions $f, f(-1)+f(0)$ lies in the interval

The function $f(x) = {x^{1/x}}$ is

${\cot ^{ - 1}}\frac{3}{4} + {\sin ^{ - 1}}\frac{5}{{13}} = $

The equation of the normal to the curve y = x(2 - x) at the point (2, 0) is:

Range of $\text{f(x)}=\sqrt{(1-\cos\text{x})\sqrt{(1-\cos\text{x})\sqrt{(1-\cos\text{x}).....\infty}}}$

The two parts of $100 $ for which the sum of double of first and square of second part is minimum, are

Let $A =\{2,3,4\}$ and $B =\{8,9,12\}$. Then the number of elements in the relation $R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right.$ divides $b_2$ and $a_2$ divides $\left.b_1\right\}$ is:

If $[.]$ represents the greatest integer function, then the value of $\int_{0}^{\sqrt{\pi / 2}}\left(\left[ x ^{2}\right]+[-\cos x ]\right) d x$ is.............

The maximum area of a right angled triangle with hypotenuse $h$ is