Aspire Faculty ID #11963 · Topic: NIMCET 2025 · Just now
NIMCET 2025

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}+\hat{k}$, then a vector of magnitude $\sqrt{22}$ which is parallel to $2\vec{a}-\vec{b}+3\vec{c}$ is

Solution

Given: $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ 
$\vec{b} = 2\hat{i} - \hat{j} + 3\hat{k}$ 
$\vec{c} = \hat{i} - 2\hat{j} + \hat{k}$ 

Compute: $2\vec{a} - \vec{b} + 3\vec{c}$ 

First: 
$2\vec{a} = 2\hat{i} + 2\hat{j} + 2\hat{k}$ 
$-\vec{b} = -2\hat{i} + \hat{j} - 3\hat{k}$ 
$3\vec{c} = 3\hat{i} - 6\hat{j} + 3\hat{k}$ 

Add components: 
$i$–component: $2 - 2 + 3 = 3$ 
$j$–component: $2 + 1 - 6 = -3$ 
$k$–component: $2 - 3 + 3 = 2$ 
So the vector: $\vec{v} = 3\hat{i} - 3\hat{j} + 2\hat{k}$ 
Its magnitude: $|\vec{v}| = \sqrt{3^2 + (-3)^2 + 2^2} = \sqrt{9 + 9 + 4} = \sqrt{22}$ 
We need a vector parallel to $\vec{v}$ with magnitude $\sqrt{22}$. 
Since $|\vec{v}| = \sqrt{22}$, the required vector is simply: $\boxed{3\hat{i} - 3\hat{j} + 2\hat{k}}$
← Previous Next →

Previous 10 Questions — NIMCET 2025

Nearest first
1
If $\vec{a}$ and $\vec{b}$ are twp vectors such that |$\vec{a}$|=3, |$\vec{b}$|=4 and |$\vec{a}+\vec{b}$|=1, then the v…
Topic: NIMCET 2025
 2
A tower subtends angles $\alpha, 2\alpha$ and $3\alpha$ respectively at points A, B and C which are lying on a horizont…
Topic: NIMCET 2025
 3
Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be unit vectors such that the angle between them is ${\cos }^{-1}\Bigg…
Topic: NIMCET 2025
 4
Let $A=\{{5}^n-4n-1\colon n\in N\}$ and $B=\{{}16(n-1)\colon n\in N\}$ be sets. Then
Topic: NIMCET 2025
 5
If x, y and z are three cube roots of 27, then  the determinant of the matrix $\begin{bmatrix}{x} & {y} &…
Topic: NIMCET 2025
 6
If $\vec{a}, \vec{b}$ and $\vec{c} $ are three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ , $\vec{a}.\vec{c} = …
Topic: NIMCET 2025
 7
Let A = {1,2,3, ... , 20}. Let $R\subseteq A\times A$ such that R = {(x,y): y = 2x - 7}. Then the number of elements in…
Topic: NIMCET 2025
 8
The number of all even integers between 99 and 999 which are not multiple of 3 and 5 is
Topic: NIMCET 2025
 9
There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and for red coin, it is 0.01.…
Topic: NIMCET 2025
 10
The value of $\frac{d}{dx}\int ^{2\sin x}_{\sin {x}^2}{e}^{{t}^2}dt$ at $x=\pi$
Topic: NIMCET 2025

Next 10 Questions — NIMCET 2025

Ascending by ID
1
Consider the sample space $\Omega={\{(x,y):x,y\in{\{1,2,3,4\}\}}}$ where each outcome is equally likely. Let A = {x ≥ 2…
Topic: NIMCET 2025
 2
Let the line $\frac{x}{4}+\frac{y}{2}=1$ meets the x-axis and y-axis at A and B, respectively. M is the midpoint of sid…
Topic: NIMCET 2025
 3
Which one of the following is NOT a correct statement?
Topic: NIMCET 2025
 4
An equilateral triangle is inscribed in the parabola $y^2 = x$. One vertex of the triangle is at the vertex of the para…
Topic: NIMCET 2025
 5
The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° …
Topic: NIMCET 2025
 6
The number of accidents per week in a town follows Poisson distribution with mean 3 (In Exam Given 2, which is incorrec…
Topic: NIMCET 2025
 7
If $B=sin^2 y+cos^4 y$, then for all real y
Topic: NIMCET 2025
 8
Let $F_1, F_2$ be foci of hyperbola $\frac{{x}^2}{{a}^2}-\frac{{y}^2}{{b}^2}=1$, a>0, b>0, and let O be…
Topic: NIMCET 2025
 9
A circle with its center in the first quadrant touches both the coordinate axes and the line x-y-2=0. Then the area of …
Topic: NIMCET 2025
 10
If $\alpha$ and $\beta$ are the two roots of the quadratic equation $x^2 + ax + b = 0, (ab \ne 0)$ then the quadratic r…
Topic: NIMCET 2025
Ask Your Question or Put Your Review.

loading...