If the vectors 3 i+ j+k and 2 i-j+8 k are perpendicular, then is … - Vidyadip

Question

If the vectors $3 \hat{i}+\lambda \hat{j}+\hat{k}$ and $2 \hat{i}-\hat{j}+8 \hat{k}$ are perpendicular, then $\lambda$ is equal to

✓

Answer

$(d) 14$
Explanation: given vectors $3 \hat{i}+\lambda \hat{j}+\hat{k}$ and $2 \hat{i}-\hat{j}+8 \hat{k}$ are perpendicular to each other
$ \Longrightarrow(3 \hat{i}+\lambda \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+8 \hat{k})=0$
$\Longrightarrow 6-\lambda+8=0 \Longrightarrow \lambda=14$

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 Model Paper 2→Model Paper 2 — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The value of $\Delta=\left|\begin{array}{ccc}0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0\end{array}\right|$ is

If $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},\text{J}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix},$ then B equals:

$\text{I}\cos\theta+\text{J}\sin\theta$
$\text{I}\sin\theta+\text{J}\cos\theta$
$\text{I}\cos\theta-\text{J}\sin\theta$
$-\text{I}\cos\theta+\text{J}\sin\theta$

The real function $f(x)=2 x^3-3 x^2-36 x+7$ is

If A and B are two events such that $\text{P}(\text{A}|\text{B})=\text{p},\text{P(A)}=\text{p},\text{P(B)}=\frac{1}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then p =

$\frac{2}{3}$
$\frac{3}{5}$
$\frac{1}{3}$
$\frac{3}{4}$

Three faces of aj ordinary dice are yellow, two faces are red and one face is blue. The dice is rolled 3 times. The probability that yellow red and blue face appear in the first second and third throws respectively, is

$\frac{1}{36}$
$\frac{1}{6}$
$\frac{1}{30}$
None of these.

The distance of the plane through the intersection of the planes ax + by + cz +d = 0 and lx + my + nz + P = 0 and parallel to the line y = 0, z = 0

(bl - am)y + (cl - an)z + dl - ap = 0
(am - bl)x + (mc - bn)z + md - bp = 0
(na - cl)x + (bn - cm)y + nd - cp = 0
None of these

The area bounded by lines y=x and x = 2 in first quadrant is

Which of the following functions from $\text{A}=\{\text{x}\in\text{R}:-1\leq\text{x}\leq1\}$ to itself are bijections?

$\text{f(x)}=|\text{x}|$
$\text{f(x)}=\sin\frac{\pi\text{x}}{2}$
$\text{f(x)}=\sin\frac{\pi\text{x}}{4}$
$\text{None of these}$

The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80, x, y ≥ 0 is:

320
300
230
none of these

Choose the correct answer from the given four options:The area of the region bounded by parabola $y^2 = x$ and the straight line $2y = x$ is: