Scalar (dot) Product of Vector
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Vector Algebra

88010 If \(\vec{a}, \vec{b}, \vec{c}\) are position vectors of the vertices of a triangle, then its area is

1 \(\frac{1}{2}|\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}|\)
2 \(\frac{1}{2}|\vec{a} \times(\vec{b} \times \vec{c})|\)
3 \(\frac{1}{2}|\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}|\)
4 \(\frac{1}{2}|\overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})|\)
AMU-2006
Vector Algebra

88011 The angle between the vectors \((2 \hat{i}+6 \hat{j}+3 \hat{k})\) and \((12 \hat{i}-4 \hat{j}+3 \hat{k})\) is

1 \(\cos ^{-1}\left(\frac{1}{9}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{11}\right)\)
3 \(\cos ^{-1}\left(\frac{9}{91}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{10}\right)\)
AMU-2002
Vector Algebra

88012 If \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}+\hat{j}+2 \hat{k}\), then the unit vector perpendicular to \(\vec{a}\) and \(\vec{b}\) is

1 \(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{3}}\)
2 \(\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\)
3 \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
4 \(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\)
AMU-2002
Vector Algebra

88013 The area of a parallelogram whose adjacent sides are \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{k}}\) is

1 \(10 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(5 \sqrt{6}\)
4 \(10 \sqrt{6}\)
AMU-2002
Vector Algebra

88014 Let
\(\mathbf{u}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{v}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(w=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{k}\). If \(\hat{\mathbf{n}}\) is \(a\) unit vector such that \(\mathbf{u} \times \hat{\mathbf{n}}=\mathbf{0}\) and \(\mathbf{v} \times \hat{\mathbf{n}}=\mathbf{0}\), then \(|\mathbf{w} \times \hat{\mathbf{n}}|\) is equal to

1 0
2 1
3 2
4 3
CG PET-2005
NEET DIGITAL LIBRARY
Vector Algebra

88010 If \(\vec{a}, \vec{b}, \vec{c}\) are position vectors of the vertices of a triangle, then its area is

1 \(\frac{1}{2}|\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}|\)
2 \(\frac{1}{2}|\vec{a} \times(\vec{b} \times \vec{c})|\)
3 \(\frac{1}{2}|\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}|\)
4 \(\frac{1}{2}|\overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})|\)
AMU-2006
Vector Algebra

88011 The angle between the vectors \((2 \hat{i}+6 \hat{j}+3 \hat{k})\) and \((12 \hat{i}-4 \hat{j}+3 \hat{k})\) is

1 \(\cos ^{-1}\left(\frac{1}{9}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{11}\right)\)
3 \(\cos ^{-1}\left(\frac{9}{91}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{10}\right)\)
AMU-2002
Vector Algebra

88012 If \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}+\hat{j}+2 \hat{k}\), then the unit vector perpendicular to \(\vec{a}\) and \(\vec{b}\) is

1 \(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{3}}\)
2 \(\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\)
3 \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
4 \(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\)
AMU-2002
Vector Algebra

88013 The area of a parallelogram whose adjacent sides are \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{k}}\) is

1 \(10 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(5 \sqrt{6}\)
4 \(10 \sqrt{6}\)
AMU-2002
Vector Algebra

88014 Let
\(\mathbf{u}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{v}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(w=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{k}\). If \(\hat{\mathbf{n}}\) is \(a\) unit vector such that \(\mathbf{u} \times \hat{\mathbf{n}}=\mathbf{0}\) and \(\mathbf{v} \times \hat{\mathbf{n}}=\mathbf{0}\), then \(|\mathbf{w} \times \hat{\mathbf{n}}|\) is equal to

1 0
2 1
3 2
4 3
CG PET-2005
Join With Us for More Updates
Vector Algebra

88010 If \(\vec{a}, \vec{b}, \vec{c}\) are position vectors of the vertices of a triangle, then its area is

1 \(\frac{1}{2}|\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}|\)
2 \(\frac{1}{2}|\vec{a} \times(\vec{b} \times \vec{c})|\)
3 \(\frac{1}{2}|\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}|\)
4 \(\frac{1}{2}|\overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})|\)
AMU-2006
Vector Algebra

88011 The angle between the vectors \((2 \hat{i}+6 \hat{j}+3 \hat{k})\) and \((12 \hat{i}-4 \hat{j}+3 \hat{k})\) is

1 \(\cos ^{-1}\left(\frac{1}{9}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{11}\right)\)
3 \(\cos ^{-1}\left(\frac{9}{91}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{10}\right)\)
AMU-2002
Vector Algebra

88012 If \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}+\hat{j}+2 \hat{k}\), then the unit vector perpendicular to \(\vec{a}\) and \(\vec{b}\) is

1 \(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{3}}\)
2 \(\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\)
3 \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
4 \(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\)
AMU-2002
Vector Algebra

88013 The area of a parallelogram whose adjacent sides are \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{k}}\) is

1 \(10 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(5 \sqrt{6}\)
4 \(10 \sqrt{6}\)
AMU-2002
Vector Algebra

88014 Let
\(\mathbf{u}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{v}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(w=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{k}\). If \(\hat{\mathbf{n}}\) is \(a\) unit vector such that \(\mathbf{u} \times \hat{\mathbf{n}}=\mathbf{0}\) and \(\mathbf{v} \times \hat{\mathbf{n}}=\mathbf{0}\), then \(|\mathbf{w} \times \hat{\mathbf{n}}|\) is equal to

1 0
2 1
3 2
4 3
CG PET-2005
For More Updates join with Us
Vector Algebra

88010 If \(\vec{a}, \vec{b}, \vec{c}\) are position vectors of the vertices of a triangle, then its area is

1 \(\frac{1}{2}|\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}|\)
2 \(\frac{1}{2}|\vec{a} \times(\vec{b} \times \vec{c})|\)
3 \(\frac{1}{2}|\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}|\)
4 \(\frac{1}{2}|\overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})|\)
AMU-2006
Vector Algebra

88011 The angle between the vectors \((2 \hat{i}+6 \hat{j}+3 \hat{k})\) and \((12 \hat{i}-4 \hat{j}+3 \hat{k})\) is

1 \(\cos ^{-1}\left(\frac{1}{9}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{11}\right)\)
3 \(\cos ^{-1}\left(\frac{9}{91}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{10}\right)\)
AMU-2002
Vector Algebra

88012 If \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}+\hat{j}+2 \hat{k}\), then the unit vector perpendicular to \(\vec{a}\) and \(\vec{b}\) is

1 \(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{3}}\)
2 \(\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\)
3 \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
4 \(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\)
AMU-2002
Vector Algebra

88013 The area of a parallelogram whose adjacent sides are \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{k}}\) is

1 \(10 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(5 \sqrt{6}\)
4 \(10 \sqrt{6}\)
AMU-2002
Vector Algebra

88014 Let
\(\mathbf{u}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{v}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(w=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{k}\). If \(\hat{\mathbf{n}}\) is \(a\) unit vector such that \(\mathbf{u} \times \hat{\mathbf{n}}=\mathbf{0}\) and \(\mathbf{v} \times \hat{\mathbf{n}}=\mathbf{0}\), then \(|\mathbf{w} \times \hat{\mathbf{n}}|\) is equal to

1 0
2 1
3 2
4 3
CG PET-2005
NEET DIGITAL LIBRARY
Vector Algebra

88010 If \(\vec{a}, \vec{b}, \vec{c}\) are position vectors of the vertices of a triangle, then its area is

1 \(\frac{1}{2}|\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}|\)
2 \(\frac{1}{2}|\vec{a} \times(\vec{b} \times \vec{c})|\)
3 \(\frac{1}{2}|\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}|\)
4 \(\frac{1}{2}|\overrightarrow{\mathrm{a}} \cdot(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})|\)
AMU-2006
Vector Algebra

88011 The angle between the vectors \((2 \hat{i}+6 \hat{j}+3 \hat{k})\) and \((12 \hat{i}-4 \hat{j}+3 \hat{k})\) is

1 \(\cos ^{-1}\left(\frac{1}{9}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{11}\right)\)
3 \(\cos ^{-1}\left(\frac{9}{91}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{10}\right)\)
AMU-2002
Vector Algebra

88012 If \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}+\hat{j}+2 \hat{k}\), then the unit vector perpendicular to \(\vec{a}\) and \(\vec{b}\) is

1 \(\frac{\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{3}}\)
2 \(\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\)
3 \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
4 \(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{3}}\)
AMU-2002
Vector Algebra

88013 The area of a parallelogram whose adjacent sides are \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{k}}\) is

1 \(10 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(5 \sqrt{6}\)
4 \(10 \sqrt{6}\)
AMU-2002
Vector Algebra

88014 Let
\(\mathbf{u}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{v}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(w=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{k}\). If \(\hat{\mathbf{n}}\) is \(a\) unit vector such that \(\mathbf{u} \times \hat{\mathbf{n}}=\mathbf{0}\) and \(\mathbf{v} \times \hat{\mathbf{n}}=\mathbf{0}\), then \(|\mathbf{w} \times \hat{\mathbf{n}}|\) is equal to

1 0
2 1
3 2
4 3
CG PET-2005