SCALAR PRODUCT (OR) DOT PRODUCT
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VECTORS

268990 The angle between the diagonals of a cube with edges of unit length is

1 \(\sin ^{-1}(1 / 3)\)
2 \(\cos ^{-1}(1 / 3)\)
3 \(\tan ^{-1}(1 / 3)\)
4 \(\cot ^{-1}(1 / 3)\)
VECTORS

268991 The angle made by the vector \(\vec{A}=2 \hat{i}+3 \hat{j}\) with \(\mathrm{Y}\)-axis is

1 \(\tan ^{-1} \square^{-3} \theta\)
2 \(\tan ^{-1} \because^{-2} \theta\)
3 \(\sin ^{-1} \theta \frac{2}{3} \theta\)
4 \(\cos ^{-1} \square^{-\frac{3}{2}} \theta\)
VECTORS

268992 If \(l_{1}, m_{1}, n_{1}\) and \(l_{2}, m_{2}, n_{2}\) are the directional cosines of two vectors and \(\theta\) is the angle between them, then their value of \(\cos \theta\) is

1 \(l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}\)
2 \(l_{1} m_{1}+m_{1} n_{1}+n_{1} l_{1}\)
3 \(l_{2} m_{2}+m_{2} n_{2}+n_{2} l_{2}\)
4 \(m_{1} l_{2}+l_{2} m_{2}+n_{1} m_{2}\)
VECTORS

268993 If \(\vec{A}+\vec{B}=\vec{C}\), then magnitude of \(\vec{B}\) is

1 \(\vec{C}-\vec{A}\)
2 \(C-A\)
3 \(\sqrt{\bar{C} . \vec{B}-\vec{A} \cdot \vec{B}}\)
4 \(\sqrt{\bar{C} . \vec{A}-\vec{B} \cdot \vec{A}}\)
VECTORS

268994 If \(\vec{a}=m \vec{b}+\vec{c}\). The scalar \(m\) is

1 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{b^{2}}\)
2 \(\frac{\vec{c} \cdot \vec{b}-\vec{a} \cdot \vec{c}}{a^{2}}\)
3 \(\frac{\vec{c} \cdot \vec{a}-\vec{b} \cdot \vec{c}}{c^{2}}\)
4 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{a^{2}}\)
NEET DIGITAL LIBRARY
VECTORS

268990 The angle between the diagonals of a cube with edges of unit length is

1 \(\sin ^{-1}(1 / 3)\)
2 \(\cos ^{-1}(1 / 3)\)
3 \(\tan ^{-1}(1 / 3)\)
4 \(\cot ^{-1}(1 / 3)\)
VECTORS

268991 The angle made by the vector \(\vec{A}=2 \hat{i}+3 \hat{j}\) with \(\mathrm{Y}\)-axis is

1 \(\tan ^{-1} \square^{-3} \theta\)
2 \(\tan ^{-1} \because^{-2} \theta\)
3 \(\sin ^{-1} \theta \frac{2}{3} \theta\)
4 \(\cos ^{-1} \square^{-\frac{3}{2}} \theta\)
VECTORS

268992 If \(l_{1}, m_{1}, n_{1}\) and \(l_{2}, m_{2}, n_{2}\) are the directional cosines of two vectors and \(\theta\) is the angle between them, then their value of \(\cos \theta\) is

1 \(l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}\)
2 \(l_{1} m_{1}+m_{1} n_{1}+n_{1} l_{1}\)
3 \(l_{2} m_{2}+m_{2} n_{2}+n_{2} l_{2}\)
4 \(m_{1} l_{2}+l_{2} m_{2}+n_{1} m_{2}\)
VECTORS

268993 If \(\vec{A}+\vec{B}=\vec{C}\), then magnitude of \(\vec{B}\) is

1 \(\vec{C}-\vec{A}\)
2 \(C-A\)
3 \(\sqrt{\bar{C} . \vec{B}-\vec{A} \cdot \vec{B}}\)
4 \(\sqrt{\bar{C} . \vec{A}-\vec{B} \cdot \vec{A}}\)
VECTORS

268994 If \(\vec{a}=m \vec{b}+\vec{c}\). The scalar \(m\) is

1 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{b^{2}}\)
2 \(\frac{\vec{c} \cdot \vec{b}-\vec{a} \cdot \vec{c}}{a^{2}}\)
3 \(\frac{\vec{c} \cdot \vec{a}-\vec{b} \cdot \vec{c}}{c^{2}}\)
4 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{a^{2}}\)
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VECTORS

268990 The angle between the diagonals of a cube with edges of unit length is

1 \(\sin ^{-1}(1 / 3)\)
2 \(\cos ^{-1}(1 / 3)\)
3 \(\tan ^{-1}(1 / 3)\)
4 \(\cot ^{-1}(1 / 3)\)
VECTORS

268991 The angle made by the vector \(\vec{A}=2 \hat{i}+3 \hat{j}\) with \(\mathrm{Y}\)-axis is

1 \(\tan ^{-1} \square^{-3} \theta\)
2 \(\tan ^{-1} \because^{-2} \theta\)
3 \(\sin ^{-1} \theta \frac{2}{3} \theta\)
4 \(\cos ^{-1} \square^{-\frac{3}{2}} \theta\)
VECTORS

268992 If \(l_{1}, m_{1}, n_{1}\) and \(l_{2}, m_{2}, n_{2}\) are the directional cosines of two vectors and \(\theta\) is the angle between them, then their value of \(\cos \theta\) is

1 \(l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}\)
2 \(l_{1} m_{1}+m_{1} n_{1}+n_{1} l_{1}\)
3 \(l_{2} m_{2}+m_{2} n_{2}+n_{2} l_{2}\)
4 \(m_{1} l_{2}+l_{2} m_{2}+n_{1} m_{2}\)
VECTORS

268993 If \(\vec{A}+\vec{B}=\vec{C}\), then magnitude of \(\vec{B}\) is

1 \(\vec{C}-\vec{A}\)
2 \(C-A\)
3 \(\sqrt{\bar{C} . \vec{B}-\vec{A} \cdot \vec{B}}\)
4 \(\sqrt{\bar{C} . \vec{A}-\vec{B} \cdot \vec{A}}\)
VECTORS

268994 If \(\vec{a}=m \vec{b}+\vec{c}\). The scalar \(m\) is

1 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{b^{2}}\)
2 \(\frac{\vec{c} \cdot \vec{b}-\vec{a} \cdot \vec{c}}{a^{2}}\)
3 \(\frac{\vec{c} \cdot \vec{a}-\vec{b} \cdot \vec{c}}{c^{2}}\)
4 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{a^{2}}\)
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VECTORS

268990 The angle between the diagonals of a cube with edges of unit length is

1 \(\sin ^{-1}(1 / 3)\)
2 \(\cos ^{-1}(1 / 3)\)
3 \(\tan ^{-1}(1 / 3)\)
4 \(\cot ^{-1}(1 / 3)\)
VECTORS

268991 The angle made by the vector \(\vec{A}=2 \hat{i}+3 \hat{j}\) with \(\mathrm{Y}\)-axis is

1 \(\tan ^{-1} \square^{-3} \theta\)
2 \(\tan ^{-1} \because^{-2} \theta\)
3 \(\sin ^{-1} \theta \frac{2}{3} \theta\)
4 \(\cos ^{-1} \square^{-\frac{3}{2}} \theta\)
VECTORS

268992 If \(l_{1}, m_{1}, n_{1}\) and \(l_{2}, m_{2}, n_{2}\) are the directional cosines of two vectors and \(\theta\) is the angle between them, then their value of \(\cos \theta\) is

1 \(l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}\)
2 \(l_{1} m_{1}+m_{1} n_{1}+n_{1} l_{1}\)
3 \(l_{2} m_{2}+m_{2} n_{2}+n_{2} l_{2}\)
4 \(m_{1} l_{2}+l_{2} m_{2}+n_{1} m_{2}\)
VECTORS

268993 If \(\vec{A}+\vec{B}=\vec{C}\), then magnitude of \(\vec{B}\) is

1 \(\vec{C}-\vec{A}\)
2 \(C-A\)
3 \(\sqrt{\bar{C} . \vec{B}-\vec{A} \cdot \vec{B}}\)
4 \(\sqrt{\bar{C} . \vec{A}-\vec{B} \cdot \vec{A}}\)
VECTORS

268994 If \(\vec{a}=m \vec{b}+\vec{c}\). The scalar \(m\) is

1 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{b^{2}}\)
2 \(\frac{\vec{c} \cdot \vec{b}-\vec{a} \cdot \vec{c}}{a^{2}}\)
3 \(\frac{\vec{c} \cdot \vec{a}-\vec{b} \cdot \vec{c}}{c^{2}}\)
4 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{a^{2}}\)
NEET DIGITAL LIBRARY
VECTORS

268990 The angle between the diagonals of a cube with edges of unit length is

1 \(\sin ^{-1}(1 / 3)\)
2 \(\cos ^{-1}(1 / 3)\)
3 \(\tan ^{-1}(1 / 3)\)
4 \(\cot ^{-1}(1 / 3)\)
VECTORS

268991 The angle made by the vector \(\vec{A}=2 \hat{i}+3 \hat{j}\) with \(\mathrm{Y}\)-axis is

1 \(\tan ^{-1} \square^{-3} \theta\)
2 \(\tan ^{-1} \because^{-2} \theta\)
3 \(\sin ^{-1} \theta \frac{2}{3} \theta\)
4 \(\cos ^{-1} \square^{-\frac{3}{2}} \theta\)
VECTORS

268992 If \(l_{1}, m_{1}, n_{1}\) and \(l_{2}, m_{2}, n_{2}\) are the directional cosines of two vectors and \(\theta\) is the angle between them, then their value of \(\cos \theta\) is

1 \(l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}\)
2 \(l_{1} m_{1}+m_{1} n_{1}+n_{1} l_{1}\)
3 \(l_{2} m_{2}+m_{2} n_{2}+n_{2} l_{2}\)
4 \(m_{1} l_{2}+l_{2} m_{2}+n_{1} m_{2}\)
VECTORS

268993 If \(\vec{A}+\vec{B}=\vec{C}\), then magnitude of \(\vec{B}\) is

1 \(\vec{C}-\vec{A}\)
2 \(C-A\)
3 \(\sqrt{\bar{C} . \vec{B}-\vec{A} \cdot \vec{B}}\)
4 \(\sqrt{\bar{C} . \vec{A}-\vec{B} \cdot \vec{A}}\)
VECTORS

268994 If \(\vec{a}=m \vec{b}+\vec{c}\). The scalar \(m\) is

1 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{b^{2}}\)
2 \(\frac{\vec{c} \cdot \vec{b}-\vec{a} \cdot \vec{c}}{a^{2}}\)
3 \(\frac{\vec{c} \cdot \vec{a}-\vec{b} \cdot \vec{c}}{c^{2}}\)
4 \(\frac{\vec{a} \cdot \vec{b}-\vec{b} \cdot \vec{c}}{a^{2}}\)