ADDITION,SUBTRACTIONAND RESOLUTION OF VECTORS
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VECTORS

268960 A bird moves in such a way that it has a displacement of \(12 \mathrm{~m}\) towards east, \(5 \mathrm{~m}\) towards north and \(9 \mathrm{~m}\) vertically upwards. Find the magnitude of its displacement

1 \(5 \sqrt{2} m\)
2 \(5 \sqrt{10} \mathrm{~m}\)
3 \(5 \sqrt{5} \mathrm{~m}\)
4 \(5 \mathrm{~m}\)
VECTORS

268961 An aeroplane is heading north east at a speed of \(141.4 \mathrm{~ms}^{-1}\). The northward component of its velocity is

1 \(141.4 \mathrm{~ms}^{-1}\)
2 \(100 \mathrm{~ms}^{-1}\)
3 \(zero\)
4 \(50 \mathrm{~ms}^{-1}\)
VECTORS

268962 The unit vector parallel to the resultant of the vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is

1 \(\frac{1}{7} \mathrm{~B}^{3} \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)
2 \(\frac{1}{7} \beta_{3} \hat{i}+6 \hat{j}+2 \hat{k}\)
3 \(\frac{1}{49} \beta_{3} \hat{i}+6 \hat{j}-2 \hat{k}\)目
4 \(\frac{1}{49}{ }^{3} \hat{i}-6 \hat{j}+2 \hat{k}\)
VECTORS

268963 The vector parallel to \(4 \hat{i}-3 \hat{j}+5 \hat{k}\) and whose length is the arithmetic mean of lengths of two vectors \(2 \hat{i}-4 \hat{j}+4 \hat{k}\) and \(\hat{i}+\sqrt{6} \hat{j}+3 \hat{k}\) is

1 \(4 \hat{i}-3 \hat{j}+5 \hat{k}\)
2 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{3}\)
3 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{2}\)
4 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{5}\)
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VECTORS

268960 A bird moves in such a way that it has a displacement of \(12 \mathrm{~m}\) towards east, \(5 \mathrm{~m}\) towards north and \(9 \mathrm{~m}\) vertically upwards. Find the magnitude of its displacement

1 \(5 \sqrt{2} m\)
2 \(5 \sqrt{10} \mathrm{~m}\)
3 \(5 \sqrt{5} \mathrm{~m}\)
4 \(5 \mathrm{~m}\)
VECTORS

268961 An aeroplane is heading north east at a speed of \(141.4 \mathrm{~ms}^{-1}\). The northward component of its velocity is

1 \(141.4 \mathrm{~ms}^{-1}\)
2 \(100 \mathrm{~ms}^{-1}\)
3 \(zero\)
4 \(50 \mathrm{~ms}^{-1}\)
VECTORS

268962 The unit vector parallel to the resultant of the vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is

1 \(\frac{1}{7} \mathrm{~B}^{3} \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)
2 \(\frac{1}{7} \beta_{3} \hat{i}+6 \hat{j}+2 \hat{k}\)
3 \(\frac{1}{49} \beta_{3} \hat{i}+6 \hat{j}-2 \hat{k}\)目
4 \(\frac{1}{49}{ }^{3} \hat{i}-6 \hat{j}+2 \hat{k}\)
VECTORS

268963 The vector parallel to \(4 \hat{i}-3 \hat{j}+5 \hat{k}\) and whose length is the arithmetic mean of lengths of two vectors \(2 \hat{i}-4 \hat{j}+4 \hat{k}\) and \(\hat{i}+\sqrt{6} \hat{j}+3 \hat{k}\) is

1 \(4 \hat{i}-3 \hat{j}+5 \hat{k}\)
2 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{3}\)
3 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{2}\)
4 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{5}\)
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VECTORS

268960 A bird moves in such a way that it has a displacement of \(12 \mathrm{~m}\) towards east, \(5 \mathrm{~m}\) towards north and \(9 \mathrm{~m}\) vertically upwards. Find the magnitude of its displacement

1 \(5 \sqrt{2} m\)
2 \(5 \sqrt{10} \mathrm{~m}\)
3 \(5 \sqrt{5} \mathrm{~m}\)
4 \(5 \mathrm{~m}\)
VECTORS

268961 An aeroplane is heading north east at a speed of \(141.4 \mathrm{~ms}^{-1}\). The northward component of its velocity is

1 \(141.4 \mathrm{~ms}^{-1}\)
2 \(100 \mathrm{~ms}^{-1}\)
3 \(zero\)
4 \(50 \mathrm{~ms}^{-1}\)
VECTORS

268962 The unit vector parallel to the resultant of the vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is

1 \(\frac{1}{7} \mathrm{~B}^{3} \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)
2 \(\frac{1}{7} \beta_{3} \hat{i}+6 \hat{j}+2 \hat{k}\)
3 \(\frac{1}{49} \beta_{3} \hat{i}+6 \hat{j}-2 \hat{k}\)目
4 \(\frac{1}{49}{ }^{3} \hat{i}-6 \hat{j}+2 \hat{k}\)
VECTORS

268963 The vector parallel to \(4 \hat{i}-3 \hat{j}+5 \hat{k}\) and whose length is the arithmetic mean of lengths of two vectors \(2 \hat{i}-4 \hat{j}+4 \hat{k}\) and \(\hat{i}+\sqrt{6} \hat{j}+3 \hat{k}\) is

1 \(4 \hat{i}-3 \hat{j}+5 \hat{k}\)
2 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{3}\)
3 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{2}\)
4 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{5}\)
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VECTORS

268960 A bird moves in such a way that it has a displacement of \(12 \mathrm{~m}\) towards east, \(5 \mathrm{~m}\) towards north and \(9 \mathrm{~m}\) vertically upwards. Find the magnitude of its displacement

1 \(5 \sqrt{2} m\)
2 \(5 \sqrt{10} \mathrm{~m}\)
3 \(5 \sqrt{5} \mathrm{~m}\)
4 \(5 \mathrm{~m}\)
VECTORS

268961 An aeroplane is heading north east at a speed of \(141.4 \mathrm{~ms}^{-1}\). The northward component of its velocity is

1 \(141.4 \mathrm{~ms}^{-1}\)
2 \(100 \mathrm{~ms}^{-1}\)
3 \(zero\)
4 \(50 \mathrm{~ms}^{-1}\)
VECTORS

268962 The unit vector parallel to the resultant of the vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is

1 \(\frac{1}{7} \mathrm{~B}^{3} \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)
2 \(\frac{1}{7} \beta_{3} \hat{i}+6 \hat{j}+2 \hat{k}\)
3 \(\frac{1}{49} \beta_{3} \hat{i}+6 \hat{j}-2 \hat{k}\)目
4 \(\frac{1}{49}{ }^{3} \hat{i}-6 \hat{j}+2 \hat{k}\)
VECTORS

268963 The vector parallel to \(4 \hat{i}-3 \hat{j}+5 \hat{k}\) and whose length is the arithmetic mean of lengths of two vectors \(2 \hat{i}-4 \hat{j}+4 \hat{k}\) and \(\hat{i}+\sqrt{6} \hat{j}+3 \hat{k}\) is

1 \(4 \hat{i}-3 \hat{j}+5 \hat{k}\)
2 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{3}\)
3 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{2}\)
4 \((4 \hat{i}-3 \hat{j}+5 \hat{k}) / \sqrt{5}\)
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