00. Scalar and Vector Quantities
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NEET DIGITAL LIBRARY
Motion in Plane

143636 Which of the following relations is true for two unit vector \(\hat{\mathbf{A}}\) and \(\hat{\mathbf{B}}\) making an angle \(\theta\) to each other?

1 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
2 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
3 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
4 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
Shift-I]
Motion in Plane

143637 Match List I with List II.
|List-I|List -II|
|
|(A) \(\mathbf{C}-\mathbf{A}-\mathbf{B}=0\)|i) original image|
|(B) \(\mathbf{A}-\mathrm{C}-\mathrm{B}=\mathbf{0}\)|ii)original image|
|(C) \(B-A-C=0\)|iii)original image|
|(D) \(\mathbf{A}+\mathbf{B}=-\mathbf{C}\)|iv)original image|
Choose the correct answer from the options given below.

1 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (i), (C) \(\rightarrow\) (iii), (D) \(\rightarrow\) (ii)
2 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (iii), (C) \(\rightarrow\) (i), (D) \(\rightarrow\) (ii)
3 (A) \(\rightarrow\) (iii), (B) \(\rightarrow\) (ii), (C) \(\rightarrow\) (iv), (D) \(\rightarrow\) (i)
4 (A) \(\rightarrow\) (i), (B) \(\rightarrow\) (iv), (C) \(\rightarrow\) (ii), (D) \(\rightarrow\) (iii)
JEE Main-25.07.2021
Motion in Plane

143638 Two vectors \(P\) and \(Q\) have equal magnitudes. If the magnitude of \(P+Q\) is \(n\) times the magnitude of \(P-Q\), then angle between \(P\) and \(Q\) is

1 \(\sin ^{-1}\left(\frac{n-1}{n+1}\right)\)
2 \(\cos ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)\)
3 \(\sin ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
4 \(\cos ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
JEE Main-25.07.2021
Motion in Plane

143639 If \(A\) and \(B\) are two vectors satisfying the relation \(\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=|\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}|\). Then, the value of \(|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\) will be

1 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}\)
2 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+\sqrt{2} \mathrm{AB}}\)
3 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB}}\)
4 \(\sqrt{A^{2}+B^{2}-\sqrt{2} A B}\)
JEE Main-20.07.2021
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Motion in Plane

143636 Which of the following relations is true for two unit vector \(\hat{\mathbf{A}}\) and \(\hat{\mathbf{B}}\) making an angle \(\theta\) to each other?

1 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
2 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
3 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
4 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
Shift-I]
Motion in Plane

143637 Match List I with List II.
|List-I|List -II|
|
|(A) \(\mathbf{C}-\mathbf{A}-\mathbf{B}=0\)|i) original image|
|(B) \(\mathbf{A}-\mathrm{C}-\mathrm{B}=\mathbf{0}\)|ii)original image|
|(C) \(B-A-C=0\)|iii)original image|
|(D) \(\mathbf{A}+\mathbf{B}=-\mathbf{C}\)|iv)original image|
Choose the correct answer from the options given below.

1 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (i), (C) \(\rightarrow\) (iii), (D) \(\rightarrow\) (ii)
2 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (iii), (C) \(\rightarrow\) (i), (D) \(\rightarrow\) (ii)
3 (A) \(\rightarrow\) (iii), (B) \(\rightarrow\) (ii), (C) \(\rightarrow\) (iv), (D) \(\rightarrow\) (i)
4 (A) \(\rightarrow\) (i), (B) \(\rightarrow\) (iv), (C) \(\rightarrow\) (ii), (D) \(\rightarrow\) (iii)
JEE Main-25.07.2021
Motion in Plane

143638 Two vectors \(P\) and \(Q\) have equal magnitudes. If the magnitude of \(P+Q\) is \(n\) times the magnitude of \(P-Q\), then angle between \(P\) and \(Q\) is

1 \(\sin ^{-1}\left(\frac{n-1}{n+1}\right)\)
2 \(\cos ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)\)
3 \(\sin ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
4 \(\cos ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
JEE Main-25.07.2021
Motion in Plane

143639 If \(A\) and \(B\) are two vectors satisfying the relation \(\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=|\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}|\). Then, the value of \(|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\) will be

1 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}\)
2 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+\sqrt{2} \mathrm{AB}}\)
3 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB}}\)
4 \(\sqrt{A^{2}+B^{2}-\sqrt{2} A B}\)
JEE Main-20.07.2021
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Motion in Plane

143636 Which of the following relations is true for two unit vector \(\hat{\mathbf{A}}\) and \(\hat{\mathbf{B}}\) making an angle \(\theta\) to each other?

1 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
2 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
3 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
4 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
Shift-I]
Motion in Plane

143637 Match List I with List II.
|List-I|List -II|
|
|(A) \(\mathbf{C}-\mathbf{A}-\mathbf{B}=0\)|i) original image|
|(B) \(\mathbf{A}-\mathrm{C}-\mathrm{B}=\mathbf{0}\)|ii)original image|
|(C) \(B-A-C=0\)|iii)original image|
|(D) \(\mathbf{A}+\mathbf{B}=-\mathbf{C}\)|iv)original image|
Choose the correct answer from the options given below.

1 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (i), (C) \(\rightarrow\) (iii), (D) \(\rightarrow\) (ii)
2 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (iii), (C) \(\rightarrow\) (i), (D) \(\rightarrow\) (ii)
3 (A) \(\rightarrow\) (iii), (B) \(\rightarrow\) (ii), (C) \(\rightarrow\) (iv), (D) \(\rightarrow\) (i)
4 (A) \(\rightarrow\) (i), (B) \(\rightarrow\) (iv), (C) \(\rightarrow\) (ii), (D) \(\rightarrow\) (iii)
JEE Main-25.07.2021
Motion in Plane

143638 Two vectors \(P\) and \(Q\) have equal magnitudes. If the magnitude of \(P+Q\) is \(n\) times the magnitude of \(P-Q\), then angle between \(P\) and \(Q\) is

1 \(\sin ^{-1}\left(\frac{n-1}{n+1}\right)\)
2 \(\cos ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)\)
3 \(\sin ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
4 \(\cos ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
JEE Main-25.07.2021
Motion in Plane

143639 If \(A\) and \(B\) are two vectors satisfying the relation \(\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=|\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}|\). Then, the value of \(|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\) will be

1 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}\)
2 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+\sqrt{2} \mathrm{AB}}\)
3 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB}}\)
4 \(\sqrt{A^{2}+B^{2}-\sqrt{2} A B}\)
JEE Main-20.07.2021
NEET DIGITAL LIBRARY
Motion in Plane

143636 Which of the following relations is true for two unit vector \(\hat{\mathbf{A}}\) and \(\hat{\mathbf{B}}\) making an angle \(\theta\) to each other?

1 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
2 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \tan \frac{\theta}{2}\)
3 \(|\hat{\mathrm{A}}+\hat{\mathrm{B}}|=|\hat{\mathrm{A}}-\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
4 \(|\hat{\mathrm{A}}-\hat{\mathrm{B}}|=|\hat{\mathrm{A}}+\hat{\mathrm{B}}| \cos \frac{\theta}{2}\)
Shift-I]
Motion in Plane

143637 Match List I with List II.
|List-I|List -II|
|
|(A) \(\mathbf{C}-\mathbf{A}-\mathbf{B}=0\)|i) original image|
|(B) \(\mathbf{A}-\mathrm{C}-\mathrm{B}=\mathbf{0}\)|ii)original image|
|(C) \(B-A-C=0\)|iii)original image|
|(D) \(\mathbf{A}+\mathbf{B}=-\mathbf{C}\)|iv)original image|
Choose the correct answer from the options given below.

1 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (i), (C) \(\rightarrow\) (iii), (D) \(\rightarrow\) (ii)
2 (A) \(\rightarrow\) (iv), (B) \(\rightarrow\) (iii), (C) \(\rightarrow\) (i), (D) \(\rightarrow\) (ii)
3 (A) \(\rightarrow\) (iii), (B) \(\rightarrow\) (ii), (C) \(\rightarrow\) (iv), (D) \(\rightarrow\) (i)
4 (A) \(\rightarrow\) (i), (B) \(\rightarrow\) (iv), (C) \(\rightarrow\) (ii), (D) \(\rightarrow\) (iii)
JEE Main-25.07.2021
Motion in Plane

143638 Two vectors \(P\) and \(Q\) have equal magnitudes. If the magnitude of \(P+Q\) is \(n\) times the magnitude of \(P-Q\), then angle between \(P\) and \(Q\) is

1 \(\sin ^{-1}\left(\frac{n-1}{n+1}\right)\)
2 \(\cos ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)\)
3 \(\sin ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
4 \(\cos ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)\)
JEE Main-25.07.2021
Motion in Plane

143639 If \(A\) and \(B\) are two vectors satisfying the relation \(\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=|\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}|\). Then, the value of \(|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\) will be

1 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}\)
2 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+\sqrt{2} \mathrm{AB}}\)
3 \(\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB}}\)
4 \(\sqrt{A^{2}+B^{2}-\sqrt{2} A B}\)
JEE Main-20.07.2021
Join With Us for More Updates