Download App

VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA1 Mark
Question
Write the value of p for which $\overrightarrow{a} = 3\hat{i} + 2\hat{j} + 9\hat{k}$ and  $\overrightarrow{b} = \hat{i} + \text{p}\hat{j} + 3\hat{k}$ are parallel vectors.
✓

Answer

Since $\overrightarrow{a} || \overrightarrow{b}$  therefore $\overrightarrow{a} = \lambda \overrightarrow{b}$$\Rightarrow (3\hat{i} + 2\hat{j} +9\hat{k} )=\lambda(\hat{i} + {p\hat{j} }+ 3\hat{k})$
$\Rightarrow \lambda = 3,\ 2 = \lambda p,\ 9 =3\lambda$
$\text{or} \lambda = 3, p = \frac{2}{3}$

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 "1 Marks Question" from VECTOR ALGEBRA→VECTOR ALGEBRA — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\vec{\text{a}}$ ia a non-zero vector of modulus a and m is a non-zero scalar such that $\text{m}\vec{\text{a}}$ is the unit vector, write the value of m.
→
$\text{If }x \in \text{N and} \begin{bmatrix} \text{x + 3} & -2 \\ \text{-3x} & \text{2x} \\ \end{bmatrix} = 8, $ then find the value of $x.$
→
$A = [a_{ij}] _{m \times n}$ is a square matrix, if
→
The binary operation * : R x R $\rightarrow$ R is defined as a * b = 2a + b. Find (2 * 3) * 4.
→
Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{e}^{\frac{\text{dy}}{\text{dx}}}=0.$ 
→
Find the second order derivatives of the function given in Exercise :
$x^{20}$
→
Find the relationship between a and b, so that the function f defined by f(x)= $ \left\{ \begin{array} { l } { a x + 1 , \text { if } x \leq 3 } \\ { b x + 3 , \text { if } x > 3 } \end{array} \right.$is continuous at x = 3.
→
Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane $\overrightarrow{\text{r}}.(\hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}) = 2.$
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+3\Big(\frac{\text{dy}}{\text{dx}}\Big)^2=\text{x}^2\log\Big(\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)$
→
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.
→