Addition and Projection of Vectors
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Vector Algebra

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

1 \(\mathrm{m}= \pm 1\)
2 \(a=\frac{1}{|\mathrm{~m}|}\)
3 \(a=|\mathrm{m}|\)
4 \(\mathrm{a}=\mathrm{m}\)
SCRA-2014
Vector Algebra

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

1 \(\frac{\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{\sqrt{62}}\)
2 \(\frac{\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{11}}\)
3 \(\frac{\hat{\mathrm{i}}+7 \hat{\mathrm{j}}}{\sqrt{50}}\)
4 \(\frac{\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\)
AMU-2018
Vector Algebra

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

1 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=\overline{\mathrm{PC}}\)
2 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=2 \overline{\mathrm{PC}}\)
3 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=-\overline{\mathrm{PC}}\)
4 \(\overline{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}=-2 \overline{\mathrm{PC}}\)
AMU-2008
Vector Algebra

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

1 \(-\frac{46}{21}\)
2 \(\frac{25}{7}\)
3 \(\frac{44}{7}\)
4 \(-\frac{88}{21}\)
AP EAMCET-2019-22.04.2019
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Vector Algebra

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

1 \(\mathrm{m}= \pm 1\)
2 \(a=\frac{1}{|\mathrm{~m}|}\)
3 \(a=|\mathrm{m}|\)
4 \(\mathrm{a}=\mathrm{m}\)
SCRA-2014
Vector Algebra

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

1 \(\frac{\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{\sqrt{62}}\)
2 \(\frac{\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{11}}\)
3 \(\frac{\hat{\mathrm{i}}+7 \hat{\mathrm{j}}}{\sqrt{50}}\)
4 \(\frac{\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\)
AMU-2018
Vector Algebra

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

1 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=\overline{\mathrm{PC}}\)
2 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=2 \overline{\mathrm{PC}}\)
3 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=-\overline{\mathrm{PC}}\)
4 \(\overline{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}=-2 \overline{\mathrm{PC}}\)
AMU-2008
Vector Algebra

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

1 \(-\frac{46}{21}\)
2 \(\frac{25}{7}\)
3 \(\frac{44}{7}\)
4 \(-\frac{88}{21}\)
AP EAMCET-2019-22.04.2019
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Vector Algebra

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

1 \(\mathrm{m}= \pm 1\)
2 \(a=\frac{1}{|\mathrm{~m}|}\)
3 \(a=|\mathrm{m}|\)
4 \(\mathrm{a}=\mathrm{m}\)
SCRA-2014
Vector Algebra

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

1 \(\frac{\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{\sqrt{62}}\)
2 \(\frac{\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{11}}\)
3 \(\frac{\hat{\mathrm{i}}+7 \hat{\mathrm{j}}}{\sqrt{50}}\)
4 \(\frac{\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\)
AMU-2018
Vector Algebra

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

1 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=\overline{\mathrm{PC}}\)
2 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=2 \overline{\mathrm{PC}}\)
3 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=-\overline{\mathrm{PC}}\)
4 \(\overline{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}=-2 \overline{\mathrm{PC}}\)
AMU-2008
Vector Algebra

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

1 \(-\frac{46}{21}\)
2 \(\frac{25}{7}\)
3 \(\frac{44}{7}\)
4 \(-\frac{88}{21}\)
AP EAMCET-2019-22.04.2019
Join With Us for More Updates
Vector Algebra

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

1 \(\mathrm{m}= \pm 1\)
2 \(a=\frac{1}{|\mathrm{~m}|}\)
3 \(a=|\mathrm{m}|\)
4 \(\mathrm{a}=\mathrm{m}\)
SCRA-2014
Vector Algebra

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

1 \(\frac{\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{\sqrt{62}}\)
2 \(\frac{\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{11}}\)
3 \(\frac{\hat{\mathrm{i}}+7 \hat{\mathrm{j}}}{\sqrt{50}}\)
4 \(\frac{\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\)
AMU-2018
Vector Algebra

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

1 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=\overline{\mathrm{PC}}\)
2 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=2 \overline{\mathrm{PC}}\)
3 \(\overline{\mathrm{PA}}+\overline{\mathrm{PB}}=-\overline{\mathrm{PC}}\)
4 \(\overline{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}=-2 \overline{\mathrm{PC}}\)
AMU-2008
Vector Algebra

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

1 \(-\frac{46}{21}\)
2 \(\frac{25}{7}\)
3 \(\frac{44}{7}\)
4 \(-\frac{88}{21}\)
AP EAMCET-2019-22.04.2019
For More Updates join with Us