MULTIPLICATION OFAVECTOR BYA SCALAR
VECTORS

268968 If \(\vec{a}=2 \hat{i}+6 \hat{j}+m \hat{k}\) and \(\vec{b}=n \hat{i}+18 \hat{j}+3 \hat{k}\) are parallel to each other then values of \(m, n\) are

1 1,6
2 6,1
3 \(-1,6\)
4 \(-1,-6\)
VECTORS

268969 A particle has an initial velocity \((6 \hat{i}+8 \hat{j}) \mathbf{m s}^{-\mathbf{1}}\) and an acceleration of \((0.8 \hat{i}+0.6 \hat{j}) \mathbf{m s}^{-2}\). Its speed after \(10 \mathrm{~s}\) is

1 \(20 \mathrm{~ms}^{-1} 2\)
2 \(7 \sqrt{2} \mathrm{~ms}^{-1}\)
3 \(10 \mathrm{~ms}^{-1}\)
4 \(14 \sqrt{2} \mathrm{~ms}^{-1}\)
\section*{SCALAR PRODUCT (OR) DOT PRODUCT}
VECTORS

268970 A motor boat is going in a river with velocity \(\vec{V}=4 \hat{i}-2 \hat{j}+\hat{k} \mathrm{~ms}^{-1}\) If the resisting force due to stream is, \(\vec{F}=(5 \hat{i}-10 \hat{j}+6 \hat{k}) N\). Then the power of the motor boat is.

1 \(100 \mathrm{w}\)
2 \(50 \mathrm{w}\)
3 \(46 \mathrm{w}\)
4 \(23 \mathrm{w}\)
VECTORS

268971 The angle between the two vectors \(-2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}+2 \hat{j}+4 \hat{k}\) is

1 \(0^{0}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 \(45^{\circ}\)
VECTORS

268972 If a vector \(\vec{A}=2 \hat{i}+2 \hat{j}+3 \hat{k}\), and \(\vec{B}=3 \hat{i}+6 \hat{j}+n \hat{k}\), are perpendicular to each other then the value of ' \(n\) ' is

1 4
2 12
3 6
4 -6
VECTORS

268968 If \(\vec{a}=2 \hat{i}+6 \hat{j}+m \hat{k}\) and \(\vec{b}=n \hat{i}+18 \hat{j}+3 \hat{k}\) are parallel to each other then values of \(m, n\) are

1 1,6
2 6,1
3 \(-1,6\)
4 \(-1,-6\)
VECTORS

268969 A particle has an initial velocity \((6 \hat{i}+8 \hat{j}) \mathbf{m s}^{-\mathbf{1}}\) and an acceleration of \((0.8 \hat{i}+0.6 \hat{j}) \mathbf{m s}^{-2}\). Its speed after \(10 \mathrm{~s}\) is

1 \(20 \mathrm{~ms}^{-1} 2\)
2 \(7 \sqrt{2} \mathrm{~ms}^{-1}\)
3 \(10 \mathrm{~ms}^{-1}\)
4 \(14 \sqrt{2} \mathrm{~ms}^{-1}\)
\section*{SCALAR PRODUCT (OR) DOT PRODUCT}
VECTORS

268970 A motor boat is going in a river with velocity \(\vec{V}=4 \hat{i}-2 \hat{j}+\hat{k} \mathrm{~ms}^{-1}\) If the resisting force due to stream is, \(\vec{F}=(5 \hat{i}-10 \hat{j}+6 \hat{k}) N\). Then the power of the motor boat is.

1 \(100 \mathrm{w}\)
2 \(50 \mathrm{w}\)
3 \(46 \mathrm{w}\)
4 \(23 \mathrm{w}\)
VECTORS

268971 The angle between the two vectors \(-2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}+2 \hat{j}+4 \hat{k}\) is

1 \(0^{0}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 \(45^{\circ}\)
VECTORS

268972 If a vector \(\vec{A}=2 \hat{i}+2 \hat{j}+3 \hat{k}\), and \(\vec{B}=3 \hat{i}+6 \hat{j}+n \hat{k}\), are perpendicular to each other then the value of ' \(n\) ' is

1 4
2 12
3 6
4 -6
VECTORS

268968 If \(\vec{a}=2 \hat{i}+6 \hat{j}+m \hat{k}\) and \(\vec{b}=n \hat{i}+18 \hat{j}+3 \hat{k}\) are parallel to each other then values of \(m, n\) are

1 1,6
2 6,1
3 \(-1,6\)
4 \(-1,-6\)
VECTORS

268969 A particle has an initial velocity \((6 \hat{i}+8 \hat{j}) \mathbf{m s}^{-\mathbf{1}}\) and an acceleration of \((0.8 \hat{i}+0.6 \hat{j}) \mathbf{m s}^{-2}\). Its speed after \(10 \mathrm{~s}\) is

1 \(20 \mathrm{~ms}^{-1} 2\)
2 \(7 \sqrt{2} \mathrm{~ms}^{-1}\)
3 \(10 \mathrm{~ms}^{-1}\)
4 \(14 \sqrt{2} \mathrm{~ms}^{-1}\)
\section*{SCALAR PRODUCT (OR) DOT PRODUCT}
VECTORS

268970 A motor boat is going in a river with velocity \(\vec{V}=4 \hat{i}-2 \hat{j}+\hat{k} \mathrm{~ms}^{-1}\) If the resisting force due to stream is, \(\vec{F}=(5 \hat{i}-10 \hat{j}+6 \hat{k}) N\). Then the power of the motor boat is.

1 \(100 \mathrm{w}\)
2 \(50 \mathrm{w}\)
3 \(46 \mathrm{w}\)
4 \(23 \mathrm{w}\)
VECTORS

268971 The angle between the two vectors \(-2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}+2 \hat{j}+4 \hat{k}\) is

1 \(0^{0}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 \(45^{\circ}\)
VECTORS

268972 If a vector \(\vec{A}=2 \hat{i}+2 \hat{j}+3 \hat{k}\), and \(\vec{B}=3 \hat{i}+6 \hat{j}+n \hat{k}\), are perpendicular to each other then the value of ' \(n\) ' is

1 4
2 12
3 6
4 -6
VECTORS

268968 If \(\vec{a}=2 \hat{i}+6 \hat{j}+m \hat{k}\) and \(\vec{b}=n \hat{i}+18 \hat{j}+3 \hat{k}\) are parallel to each other then values of \(m, n\) are

1 1,6
2 6,1
3 \(-1,6\)
4 \(-1,-6\)
VECTORS

268969 A particle has an initial velocity \((6 \hat{i}+8 \hat{j}) \mathbf{m s}^{-\mathbf{1}}\) and an acceleration of \((0.8 \hat{i}+0.6 \hat{j}) \mathbf{m s}^{-2}\). Its speed after \(10 \mathrm{~s}\) is

1 \(20 \mathrm{~ms}^{-1} 2\)
2 \(7 \sqrt{2} \mathrm{~ms}^{-1}\)
3 \(10 \mathrm{~ms}^{-1}\)
4 \(14 \sqrt{2} \mathrm{~ms}^{-1}\)
\section*{SCALAR PRODUCT (OR) DOT PRODUCT}
VECTORS

268970 A motor boat is going in a river with velocity \(\vec{V}=4 \hat{i}-2 \hat{j}+\hat{k} \mathrm{~ms}^{-1}\) If the resisting force due to stream is, \(\vec{F}=(5 \hat{i}-10 \hat{j}+6 \hat{k}) N\). Then the power of the motor boat is.

1 \(100 \mathrm{w}\)
2 \(50 \mathrm{w}\)
3 \(46 \mathrm{w}\)
4 \(23 \mathrm{w}\)
VECTORS

268971 The angle between the two vectors \(-2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}+2 \hat{j}+4 \hat{k}\) is

1 \(0^{0}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 \(45^{\circ}\)
VECTORS

268972 If a vector \(\vec{A}=2 \hat{i}+2 \hat{j}+3 \hat{k}\), and \(\vec{B}=3 \hat{i}+6 \hat{j}+n \hat{k}\), are perpendicular to each other then the value of ' \(n\) ' is

1 4
2 12
3 6
4 -6
VECTORS

268968 If \(\vec{a}=2 \hat{i}+6 \hat{j}+m \hat{k}\) and \(\vec{b}=n \hat{i}+18 \hat{j}+3 \hat{k}\) are parallel to each other then values of \(m, n\) are

1 1,6
2 6,1
3 \(-1,6\)
4 \(-1,-6\)
VECTORS

268969 A particle has an initial velocity \((6 \hat{i}+8 \hat{j}) \mathbf{m s}^{-\mathbf{1}}\) and an acceleration of \((0.8 \hat{i}+0.6 \hat{j}) \mathbf{m s}^{-2}\). Its speed after \(10 \mathrm{~s}\) is

1 \(20 \mathrm{~ms}^{-1} 2\)
2 \(7 \sqrt{2} \mathrm{~ms}^{-1}\)
3 \(10 \mathrm{~ms}^{-1}\)
4 \(14 \sqrt{2} \mathrm{~ms}^{-1}\)
\section*{SCALAR PRODUCT (OR) DOT PRODUCT}
VECTORS

268970 A motor boat is going in a river with velocity \(\vec{V}=4 \hat{i}-2 \hat{j}+\hat{k} \mathrm{~ms}^{-1}\) If the resisting force due to stream is, \(\vec{F}=(5 \hat{i}-10 \hat{j}+6 \hat{k}) N\). Then the power of the motor boat is.

1 \(100 \mathrm{w}\)
2 \(50 \mathrm{w}\)
3 \(46 \mathrm{w}\)
4 \(23 \mathrm{w}\)
VECTORS

268971 The angle between the two vectors \(-2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}+2 \hat{j}+4 \hat{k}\) is

1 \(0^{0}\)
2 \(90^{\circ}\)
3 \(180^{\circ}\)
4 \(45^{\circ}\)
VECTORS

268972 If a vector \(\vec{A}=2 \hat{i}+2 \hat{j}+3 \hat{k}\), and \(\vec{B}=3 \hat{i}+6 \hat{j}+n \hat{k}\), are perpendicular to each other then the value of ' \(n\) ' is

1 4
2 12
3 6
4 -6