Assignment Details

Vector Algebra

Note it

1469 minutes

Feb 03, 11:31 AM

30.0 marks

MCQ

30 questions

SURYA KANT SHARMA

...

Class Details

Maths

Class12th

Maths

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Question Text

Question 1 :
Given $\vec p= (2,-4,1), \vec q = (3,-1,2), \vec r = (5,5, 4)$. Then $\vec{PQ}$ and $\vec{QR}$ are

Question 3 :
Two vectors $a$ and $b$ are said to be equal, if I. $|a| = |b|$ II. they have same or parallel support. III. the same sense. Which of the following is true?

Question 5 :
When a body is thrown up, the sign of $g$ is positive when it goes up.

Question 6 :
If $\vec {a} = i + j - k, \vec {b} = 1 - j + k, \vec {c}$ is a unit vector such that $\vec {c} . \vec {a} = 0, [\vec {c} \vec {a} \vec {b}] = 0$ then a unit vectors perpendicular to both $\vec {a}$ and $\vec {c}$ is

Question 7 :
If $|\vec{a} +\vec{b}| > |\vec{a} - \vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ is

Question 8 :
Find the magnitude of two vectors $\vec a$ and $\vec b$, having the same magnitude and such that the angle between them is ${60^ \circ }$ and their scalar product is $\dfrac{1}{2}$.

Question 9 :
If $\cos \alpha, \cos \beta$ and $\cos \gamma$ are direction cosines of a vector, then they satisfy which of the following ? Prove it.

Question 10 :
A line passes through the points whose position vectors $ \hat { i } +\hat { j } -2\hat { k }$ and $\hat { i } -3\hat { j } +\hat { k }$. Then the position vector of a point on it at a unit distance from the first point is

Question 11 :
Which of the following is not a unit vector for all values of $\theta$?

Question 12 :
Given that $\vec{ A } \times \vec{ B } =\vec{ B } \times \vec { C } =\vec { 0 } $ if $\vec{ A } \vec { B } \vec { C } $ are not null vectors, Find the value of $\vec{ A } \times \vec{ C } $

Question 14 :
If $\left| {\widehat a - \widehat b} \right| = \sqrt 3 $ , then $\left| {\widehat a + \widehat b} \right|$ may be:-

Question 16 :
Four forces act on a point object. The object will be in equilibrium, if:

Question 17 :
Let $ABCD$ be a parallelogram whose diagonals intersect at $P$ and $O$ be the origin, then $\vec { OA } +\vec { OB } +\vec { OC } +\vec { OD } $ equals

Question 18 :
At what value of the parameter n the vectors $\overrightarrow{a}=\hat{i}+2\hat{j}+4\hat{k}$ and $\overrightarrow{a}=\hat{i}+2\hat{j}+2n\hat{k}$ are equal

Question 19 :
If $\bar{a}$ is unit vector, then $|\bar{a}\times \hat{i}|^2+|\bar{a}\times \hat{j}|^2+|\bar{a}\times \hat{k}|^2=$ _____________.

Question 20 :
$\vec{a},\vec{b},\vec{c}$ are three non-collinear vectors such that $\vec{a}+\vec{b}$ is parallel to $\vec{c}$ and $\vec{a}+\vec{c}$ is parallel to $\vec{b}$ then:

Question 21 :
For three vectors $\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}$ which of the following expressions is not equal to any of remaining is

Question 23 :
If the position vectors of the points $A(3,4),B(5, -6)$ and $C(4,-1)$ are $ \vec{a}, \vec{b}, \vec{c}$ respectively, compute $ \vec{a}+2\vec{b}-3\vec{c}. $

Question 24 :
The vectors $\hat { i } +2\hat { j } +3\hat { k }$, $2\hat { i } -\hat { j } +\hat { k }$ and $3\hat { i } +\hat { j } +4\hat { k }$ are so placed that the end point of one vector is the starting point of the next vector. Then the vectors are :

Question 27 :
The Polygon Law of Vector Addition is simply an extension of ____________.

Question 28 :
For non zero vectors $a,b$ and $c$, if $a+b+c=0$ then which relation true:-

Question 29 :
Express $ \vec{AB}$ in terms of unit vectors $ \hat{i} $ and $\hat{j}$, when the points are: A(4,-1), B(1,3) Find $ \left | \vec{AB} \right |$ in each case.

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