Vector Algebra Test

Result

Vector Algebra Test - 18

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Find the vector $w$ with the initial point $(4,1,2)$ and final point $(1,6,5)$ .

A
$(3,-5,-3)$

B
$(0,7,3)$

C
$(-3,5,3)$

D
None of these

Solution

Given points
$A(4,1,2)$ and $B(1,6,5)$
$\vec{OA}=4\hat{i}+\hat{j}+2\hat{k}$
$\vec{OB}=\hat{i}+6\hat{j}+5\hat{k}$
vector
$\vec{AB}=\vec{OB}-\vec{OA}$
$\vec{AB}=\hat{i}+6\hat{j}+5\hat{k}-(4\hat{i}+\hat{j}+2\hat{k})$
$\vec{AB}=\hat{i}+6\hat{j}+5\hat{k}-4\hat{i}-\hat{j}-2\hat{k}$
$\vec{AB}=-3\hat{i}+5\hat{j}+3\hat{k}$
$AB=(-3,5,3)$
Question 2
1 / -0

Find $2v$ , when $u=(3,4,-2)$ and $v=(0,-4,0)$ .

A
$(0,-8,0)$

B
$(3,8,0)$

C
$(3,-8,-2)$

D
None of these

Solution

Given points
$u(3,4,-2)$ and $v(0,-4,0)$
$\vec{u}=3\hat{i}+4\hat{j}-2\hat{k}$
$\vec{v}=-4\hat{j}$
vector
$2\vec{v}=2\times -4\vec{j}$
$2\vec{v}=-8\vec{j}=(0,-8,0)$
Question 3
1 / -0

Find the magnitude of the vector which joins the point $A$ $(4,5,6)$ to $B$ $(10,11,12)$ .

A
$12.29$

B
$10.39$

C
$10.29$

D
None of these

Solution

Given points
$A(4,5,6)$ and $B(10,11,12)$
$\vec{OA}=4\hat{i}+5\hat{j}+6\hat{k}$
$\vec{OB}=10\hat{i}+11\hat{j}+12\hat{k}$
vector
$\vec{AB}=\vec{OB}-\vec{OA}$
$\vec{AB}=10\hat{i}+11\hat{j}+12\hat{k}-(4\hat{i}+5\hat{j}+6\hat{k})$
$\vec{AB}=10\hat{i}+11\hat{j}+12\hat{k}-4\hat{i}-5\hat{j}-6\hat{k}$
$\vec{AB}=6\hat{i}+6\hat{j}+6\hat{k}$
magnitude of AB
$\left | \vec{AB} \right |=\sqrt{6^2+6^2+6^2}$

$\left | \vec{AB} \right |=\sqrt{36+36+36}$

$\left | \vec{AB} \right |=\sqrt{36\times 3}$

$\left | \vec{AB} \right |=6\sqrt{3}$

$\left | \vec{AB} \right |=6\times 1.732$

$\left | \vec{AB} \right |=10.39$
Question 4
1 / -0

Which of the following is not a unit vector for all values of $\theta$ ?

A
$(\cos\theta)i - (\sin\theta)j$

B
$(\sin\theta)i + (\cos\theta)j$

C
$(\sin2\theta)i - (\cos\theta)j$

D
$(\cos2\theta)i - (\sin2\theta)j$

Solution

Let $n$ be any vector.
Then $n$ is a unit vector, if $||n||=1$
We know that, $\cos^2 \theta + \sin^2 \theta=1$
For $n=(\sin 2\theta)i - (\cos \theta)j$
$||n||=\sin^{2} 2\theta + \cos^{2} \theta \neq 1$
Hence, $(\sin^{2} 2\theta)i + (\cos^{2} \theta)j$ is not a unit vector.
Question 5
1 / -0

Find the vector $w$ with the initial point $(8,-10,3)$ and final point $(1,10,7)$ .

A
$(7,10,-4)$

B
$(-4,10,4)$

C
$(-7,20,4)$

D
None of these

Solution

Given points
$A(8,-10,3)$ and $B(1,10,7)$
$\vec{OA}=8\hat{i}-10\hat{j}+3\hat{k}$
$\vec{OB}=\hat{i}+10\hat{j}+7\hat{k}$
vector w from A to B
$\vec{AB}=\vec{OB}-\vec{OA}$
$\vec{w}=\hat{i}+10\hat{j}+7\hat{k}-(8\hat{i}-10\hat{j}+3\hat{k})$
$\vec{w}=\hat{i}+10\hat{j}+7\hat{k}-8\hat{i}+10\hat{j}-3\hat{k}$
$\vec{AB}=-7\hat{i}+20\hat{j}+4\hat{k}=(-7,20,4)$
Question 6
1 / -0

The vector joining vector $\vec{A}$ to $\vec{B}$ is represented by:

A
$\vec{A}-\vec{B}$

B
$\vec{B}-\vec{A}$

C
$\vec{A}+\vec{B}$

D
None of these

Solution

Given vectors
$\vec{A}$ and $\vec{B}$
$\vec{AB}=\vec{B}-\vec{A}$
Question 7
1 / -0

Find the magnitude of the vector which joins the point $A$ $(-1,-3,-1)$ to $B$ $(0,0,0)$ .

A
$\sqrt{21}$

B
$\sqrt{10}$

C
$\sqrt{11}$

D
None of these

Solution

Given points
$A(-1,-3,-1)$ and $B(0,0,0)$
$\vec{OA}=-\hat{i}-3\hat{j}-\hat{k}$
$\vec{OB}=0$
vector AB from A to B
$\vec{AB}=\vec{OB}-\vec{OA}$
$\vec{AB}=0-(-\hat{i}-3\hat{j}-\hat{k})$
$\vec{AB}=+\hat{i}+3\hat{j}+\hat{k})$
magnitude of AB
$\left | \vec{AB} \right |=\sqrt{1^2+3^2+1^2}$

$\left | \vec{AB} \right |=\sqrt{1+9+1}$

$\left | \vec{AB} \right |=\sqrt{11}$
Question 8
1 / -0

Find the vector $w$ with the initial point $(a,b,c)$ and final point $(a+1,b+2,c+3)$ .

A
$(a,b+2,c+3)$

B
$(a-1,b-2,c-3)$

C
$(1,2,3)$

D
None of these

Solution

Given points
$A(a,b,c)$ and $B(a+1,b+2,c+3)$
$\vec{OA}=a\hat{i}+b\hat{j}+c\hat{k}$
$\vec{OB}=(a+1)\hat{i}+(b+2)\hat{j}+(c+3)\hat{j}$
vector $w$ from $A$ to $B$
$\vec{AB}=\vec{OB}-\vec{OA}$
$\vec{w}=(a+1)\hat{i}+(b+2)\hat{j}+(c+3)\hat{j}-(a\hat{i}+b\hat{j}+c\hat{k})$
$\vec{w}=a\hat{i}+b\hat{j}+c\hat{k}+\hat{i}+2\hat{j}+3\hat{j}-a\hat{i}-b\hat{j}-c\hat{k}$
$\vec{w}=\hat{i}+2\hat{j}+3\hat{j}=(1,2,3)$
Question 9
1 / -0

Find the magnitude of the vector which joins the point $A$ $(a,2,c)$ to $B$ $(a+1,5,c+3)$ .

A
$\sqrt{18}$

B
$\sqrt{21}$

C
$\sqrt{20}$

D
None of these

Solution

Given points
$A(a,2,c)$ and $B(a+1,5,c+3)$
$\vec{OA}=a\hat{i}+2\hat{j}+c\hat{k}$
$\vec{OB}=(a+1)\hat{i}+5\hat{j}+(c+3)\hat{j}$

$\vec{AB}=\vec{OB}-\vec{OA}$
$\vec{AB}=(a+1)\hat{i}+5\hat{j}+(c+3)\hat{j}-(a\hat{i}+2\hat{j}+c\hat{k})$
$\vec{AB}=a\hat{i}+5\hat{j}+c\hat{k}+\hat{i}+3\hat{j}-a\hat{i}-2\hat{j}-c\hat{k}$
$\vec{AB}=\hat{i}+3\hat{j}+3\hat{j}$

magnitude of AB
$\left | \vec{AB} \right |=\sqrt{1^2+3^2+3^2}$

$\left | \vec{AB} \right |=\sqrt{1+9+9}$

$\left | \vec{AB} \right |=\sqrt{19}$
none of option is matched
Question 10
1 / -0

The coordinates of a point in $3$ -D space is $(3,1,2)$ . Then the position vector of the point is:

A
$3\hat i + 3\hat j + 3\hat k$

B
$3\hat i + 2\hat j + \hat k$

C
$3\hat i + \hat j + 2\hat k$

D
$\hat i + 2\hat j + 3\hat k$

Solution

A position vector is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference.
Given point is $(3,1,2)$ in $3$ -D space.
$x,y$ and $z$ coordinates are represented by vectors $i,j$ and $k$ respectively.
Hence, position vector is given by $3\hat i+\hat j+2\hat k$ .

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Vector Algebra Test - 18

Result

Vector Algebra Test - 18

Score

-

Rank

-

SHARING IS CARING

Question 1

(3,−5,−3)(3,-5,-3)(3,−5,−3)

(0,7,3)(0,7,3)(0,7,3)

(−3,5,3)(-3,5,3)(−3,5,3)

None of these

Solution

Question 2

(0,−8,0)(0,-8,0)(0,−8,0)

(3,8,0)(3,8,0)(3,8,0)

(3,−8,−2)(3,-8,-2)(3,−8,−2)

None of these

Solution

Question 3

12.2912.2912.29

10.3910.3910.39

10.2910.2910.29

None of these

Solution

Question 4

(cos⁡θ)i−(sin⁡θ)j(\cos\theta)i - (\sin\theta)j(cosθ)i−(sinθ)j

(sin⁡θ)i+(cos⁡θ)j(\sin\theta)i + (\cos\theta)j(sinθ)i+(cosθ)j

(sin⁡2θ)i−(cos⁡θ)j(\sin2\theta)i - (\cos\theta)j(sin2θ)i−(cosθ)j

(cos⁡2θ)i−(sin⁡2θ)j(\cos2\theta)i - (\sin2\theta)j(cos2θ)i−(sin2θ)j

Solution

Question 5

(7,10,−4)(7,10,-4)(7,10,−4)

(−4,10,4)(-4,10,4)(−4,10,4)

(−7,20,4)(-7,20,4)(−7,20,4)

None of these

Solution

Question 6

A⃗−B⃗\vec{A}-\vec{B}A−B

B⃗−A⃗\vec{B}-\vec{A}B−A

A⃗+B⃗\vec{A}+\vec{B}A+B

None of these

Solution

Question 7

21\sqrt{21}21​

10\sqrt{10}10​

11\sqrt{11}11​

None of these

Solution

Question 8

(a,b+2,c+3)(a,b+2,c+3)(a,b+2,c+3)

(a−1,b−2,c−3)(a-1,b-2,c-3)(a−1,b−2,c−3)

(1,2,3)(1,2,3)(1,2,3)

None of these

Solution

Question 9

18\sqrt{18}18​

21\sqrt{21}21​

20\sqrt{20}20​

None of these

Solution

Question 10

3i^+3j^+3k^3\hat i + 3\hat j + 3\hat k3i^+3j^​+3k^

3i^+2j^+k^3\hat i + 2\hat j + \hat k3i^+2j^​+k^

3i^+j^+2k^3\hat i + \hat j + 2\hat k3i^+j^​+2k^

i^+2j^+3k^\hat i + 2\hat j + 3\hat ki^+2j^​+3k^

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.

$(3,-5,-3)$

$(0,7,3)$

$(-3,5,3)$

$(0,-8,0)$

$(3,8,0)$

$(3,-8,-2)$

$12.29$

$10.39$

$10.29$

$(\cos\theta)i - (\sin\theta)j$

$(\sin\theta)i + (\cos\theta)j$

$(\sin2\theta)i - (\cos\theta)j$

$(\cos2\theta)i - (\sin2\theta)j$

$(7,10,-4)$

$(-4,10,4)$

$(-7,20,4)$

$\vec{A}-\vec{B}$

$\vec{B}-\vec{A}$

$\vec{A}+\vec{B}$

$\sqrt{21}$

$\sqrt{10}$

$\sqrt{11}$

$(a,b+2,c+3)$

$(a-1,b-2,c-3)$

$(1,2,3)$

$\sqrt{18}$

$\sqrt{21}$

$\sqrt{20}$

$3\hat i + 3\hat j + 3\hat k$

$3\hat i + 2\hat j + \hat k$

$3\hat i + \hat j + 2\hat k$

$\hat i + 2\hat j + 3\hat k$