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Published on: 29/08/2019
Vector Algebra - I
Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
If \(\overrightarrow{a},\overrightarrow{b}\) are the position vectors A and B, then which one of the following points whose position vector lies on AB, is
\(\overrightarrow{a}+\overrightarrow{b}\)
\({2\overrightarrow{a}-\overrightarrow{b}\over 2}\)
\({2\overrightarrow{a}+\overrightarrow{b}\over 3}\)
\({\overrightarrow{a}-\overrightarrow{b}\over 3}\)
2.
One of the diagonals of parallelogram ABCD with \(\overrightarrow{a}\) and \(\overrightarrow{b}\) as adjacent sides is \(\overrightarrow{a}+\overrightarrow{b}\) The other diagonal \(\overrightarrow{BD}\) is
\(\overrightarrow{a}-\overrightarrow{b}\)
\(\overrightarrow{b}-\overrightarrow{a}\)
\(\overrightarrow{a}+\overrightarrow{b}\)
\(\overrightarrow{a}+\overrightarrow{b}\over 2\)
3.
If ABCD is a parallelogram, then \(\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}\) is equal to
\(2(\overrightarrow{AB}+\overrightarrow{AD})\)
\(4\overrightarrow{AC}\)
\(4\overrightarrow{BD}\)
\(\overrightarrow{0}\)
4.
The vectors \(\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}\) are
parallel to each other
unit vectors
mutually perpendicular vectors
coplanar vectors.
5.
A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to
\(cos^{-1}({1\over 3})\)
\(cos^{-1}({2\over 3})\)
\(cos^{-1}({1\over\sqrt 3})\)
\(cos^{-1}({2\over\sqrt 3})\)
6.
If \(\overrightarrow{BA}=3\hat{i}+2\hat{j}+\hat{k}\) and the position vector of B is \(\hat{i}+3\hat{j}-\hat{k}\) ,then the position vector of A is
\(4\hat{i}+2\hat{j}+\hat{k}\)
\(4\hat{i}+5\hat{j}\)
\(4\hat{i}\)
\(-4\hat{i}\)
7.
A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively. Then the angle between \(\overrightarrow{OP}\)and the z-axis is
45°
60°
90°
30°
8.
The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}-2\hat{j}+\hat{k}\) is
\({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)
\({2\hat{i}+\hat{j}\over\sqrt{5}}\)
\({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)
\({2\hat{i}-\hat{j}\over\sqrt{5}}\)
9.
10.
The value of \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}\) is
\(\overrightarrow{AD}\)
\(\overrightarrow{CA}\)
\(\overrightarrow{0}\)
\(-\overrightarrow{AD}\)
1.
\(\vec{m}=\frac{|\vec{b}+2 \vec{a}|}{1+2}=\frac{2 \vec{a}+\vec{b}}{3}\)
2.
\(\text { In } \Delta \mathrm{BCD}, \overrightarrow{\mathrm{BD}}=\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CD}}\)
\(=\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{a}}\)
3.
\(\overrightarrow{A B}=-\overrightarrow{C D}\)
\(\overrightarrow{A D}=\overrightarrow{B C}=-\overrightarrow{C B}\)
\(\therefore \overrightarrow{A B}+\overrightarrow{A D}+\overrightarrow{C B}+\overrightarrow{C D}=-\overrightarrow{C D}-\overrightarrow{C B}+\overrightarrow{C B}+\overrightarrow{C D}=\overrightarrow{0}\)
4.
(d)
coplanar vectors.
5.
All angle are equal
\(\therefore \alpha=\beta=\gamma\)
\(\text { W.K.T } \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1\)
\(\cos ^{2} \alpha+\cos ^{2} \alpha+\cos ^{2} \alpha =1 \)
\(3 \cos ^{2} \alpha =1 \)
\(\cos ^{2} \alpha =\frac{1}{3} \)
\(\cos \alpha =\pm \frac{1}{\sqrt{3}} \)
\(\alpha =\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
6.
\(\overrightarrow{B A}=3 \hat{i}+2 \hat{j}+\hat{k} \)
\(\overrightarrow{O A}-\overrightarrow{O B}=3 \hat{i}+2 \hat{j}+\hat{k} \)
\(\overrightarrow{O A}=3 \hat{i}+2 \hat{j}+\hat{k}+\overrightarrow{O B}=3 \hat{i}+2 \hat{j}+\hat{k}+\hat{i}+3 \hat{j}-\hat{k} \)
\(=4 \hat{i}+5 \hat{j} \)
7.
\(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \)
\(\cos ^{2} 60^{\circ}+\cos ^{2} 45^{\circ}+\cos ^{2} \gamma=1 \)
\(\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{\sqrt{2}}\right)^{2}+\cos ^{2} \gamma=1 \Rightarrow \cos ^{2} \gamma=1-\frac{1}{4}-\frac{1}{2} \)
\(\cos ^{2} \gamma=\frac{4-1-2}{4}=\frac{1}{4} \Rightarrow \cos \gamma=\frac{1}{2} \Rightarrow \gamma=60^{\circ} \)
\(\text { Angle between } \overrightarrow{O P} \text { and } z \text { axis is } 60^{\circ}\)
8.
\(\vec{a}+\vec{b} =2 \hat{i}-\hat{j} \)
\(|\vec{a}+\vec{b}| =\sqrt{4+1}=\sqrt{5} \)
\(\text { Unit vector }=\frac{2 \hat{i}-\hat{j}}{\sqrt{5}}\)
9.
(c)
10.
\(\underbrace{\overrightarrow{A B}}+ \overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{D A} \)
\(=\underbrace{\overrightarrow{A C}+\overrightarrow{C D}}+\overrightarrow{D A} \)
\(=\underbrace{\overrightarrow{A D}+\overrightarrow{D A}} \)
\(=\overrightarrow{A A}=\overrightarrow{0} . \)
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