VECTOR PRODUCT (OR) CROSS PRODUCT
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VECTORS

268982 Find the values of \(x\) and \(y\) for which vectors \(\vec{A}=6 \hat{i}+x \hat{j}-2 \hat{k}\) and \(\vec{B}=5 \hat{i}-6 \hat{j}-y \hat{k} \quad\) may be parallel

1 \(x=0, y=\frac{2}{3}\)
2 \(x=\frac{-36}{5}, y=\frac{5}{3}\)
3 \(x=\frac{-15}{3}, y=\frac{23}{5}\)
4 \(x=\frac{36}{3}, y=\frac{15}{14}\)
VECTORS

268997 The unit vector perpendicular to \(\vec{A}=2 \hat{i}+3 \hat{j}+\hat{k}\) and \(\vec{B}=\hat{i}-\hat{j}+\hat{k}\) is

1 \(\frac{4 \hat{i}-\hat{j}-5 \hat{k}}{\sqrt{42}}\)
2 \(\frac{4 \hat{i}-\hat{j}+5 \hat{k}}{\sqrt{42}}\)
3 \(\frac{4 \hat{i}+\hat{j}+5 \hat{k}}{\sqrt{42}}\)
4 \(\frac{4 \hat{i}+\hat{j}-5 \hat{k}}{\sqrt{42}}\)
VECTORS

269010 If\(\vec{A}=\frac{1}{\sqrt{2}} \cos \theta \hat{i}+\frac{1}{\sqrt{2}} \sin \theta \hat{j}\), what will be the unit vector perpendicular to \(\vec{A}\)

1 \(\cos \theta \hat{i}+\sin \hat{\theta j}\)
2 \(-\cos \theta \hat{i}+\sin \theta \hat{j}\)
3 \(\frac{\cos \theta \hat{i}+\sin \theta \hat{j}}{\sqrt{2}}\)
4 \(\sin \theta \hat{i}-\cos \hat{\theta j}\)
VECTORS

269011 \((\hat{i}+\hat{j}) \times(\hat{i}-\hat{j})=\)

1 \(-2 \hat{k}\)
2 \(2 \hat{k}\)
3 zero
4 \(2 \hat{i}\)
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VECTORS

268982 Find the values of \(x\) and \(y\) for which vectors \(\vec{A}=6 \hat{i}+x \hat{j}-2 \hat{k}\) and \(\vec{B}=5 \hat{i}-6 \hat{j}-y \hat{k} \quad\) may be parallel

1 \(x=0, y=\frac{2}{3}\)
2 \(x=\frac{-36}{5}, y=\frac{5}{3}\)
3 \(x=\frac{-15}{3}, y=\frac{23}{5}\)
4 \(x=\frac{36}{3}, y=\frac{15}{14}\)
VECTORS

268997 The unit vector perpendicular to \(\vec{A}=2 \hat{i}+3 \hat{j}+\hat{k}\) and \(\vec{B}=\hat{i}-\hat{j}+\hat{k}\) is

1 \(\frac{4 \hat{i}-\hat{j}-5 \hat{k}}{\sqrt{42}}\)
2 \(\frac{4 \hat{i}-\hat{j}+5 \hat{k}}{\sqrt{42}}\)
3 \(\frac{4 \hat{i}+\hat{j}+5 \hat{k}}{\sqrt{42}}\)
4 \(\frac{4 \hat{i}+\hat{j}-5 \hat{k}}{\sqrt{42}}\)
VECTORS

269010 If\(\vec{A}=\frac{1}{\sqrt{2}} \cos \theta \hat{i}+\frac{1}{\sqrt{2}} \sin \theta \hat{j}\), what will be the unit vector perpendicular to \(\vec{A}\)

1 \(\cos \theta \hat{i}+\sin \hat{\theta j}\)
2 \(-\cos \theta \hat{i}+\sin \theta \hat{j}\)
3 \(\frac{\cos \theta \hat{i}+\sin \theta \hat{j}}{\sqrt{2}}\)
4 \(\sin \theta \hat{i}-\cos \hat{\theta j}\)
VECTORS

269011 \((\hat{i}+\hat{j}) \times(\hat{i}-\hat{j})=\)

1 \(-2 \hat{k}\)
2 \(2 \hat{k}\)
3 zero
4 \(2 \hat{i}\)
NEET DIGITAL LIBRARY
VECTORS

268982 Find the values of \(x\) and \(y\) for which vectors \(\vec{A}=6 \hat{i}+x \hat{j}-2 \hat{k}\) and \(\vec{B}=5 \hat{i}-6 \hat{j}-y \hat{k} \quad\) may be parallel

1 \(x=0, y=\frac{2}{3}\)
2 \(x=\frac{-36}{5}, y=\frac{5}{3}\)
3 \(x=\frac{-15}{3}, y=\frac{23}{5}\)
4 \(x=\frac{36}{3}, y=\frac{15}{14}\)
VECTORS

268997 The unit vector perpendicular to \(\vec{A}=2 \hat{i}+3 \hat{j}+\hat{k}\) and \(\vec{B}=\hat{i}-\hat{j}+\hat{k}\) is

1 \(\frac{4 \hat{i}-\hat{j}-5 \hat{k}}{\sqrt{42}}\)
2 \(\frac{4 \hat{i}-\hat{j}+5 \hat{k}}{\sqrt{42}}\)
3 \(\frac{4 \hat{i}+\hat{j}+5 \hat{k}}{\sqrt{42}}\)
4 \(\frac{4 \hat{i}+\hat{j}-5 \hat{k}}{\sqrt{42}}\)
VECTORS

269010 If\(\vec{A}=\frac{1}{\sqrt{2}} \cos \theta \hat{i}+\frac{1}{\sqrt{2}} \sin \theta \hat{j}\), what will be the unit vector perpendicular to \(\vec{A}\)

1 \(\cos \theta \hat{i}+\sin \hat{\theta j}\)
2 \(-\cos \theta \hat{i}+\sin \theta \hat{j}\)
3 \(\frac{\cos \theta \hat{i}+\sin \theta \hat{j}}{\sqrt{2}}\)
4 \(\sin \theta \hat{i}-\cos \hat{\theta j}\)
VECTORS

269011 \((\hat{i}+\hat{j}) \times(\hat{i}-\hat{j})=\)

1 \(-2 \hat{k}\)
2 \(2 \hat{k}\)
3 zero
4 \(2 \hat{i}\)
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VECTORS

268982 Find the values of \(x\) and \(y\) for which vectors \(\vec{A}=6 \hat{i}+x \hat{j}-2 \hat{k}\) and \(\vec{B}=5 \hat{i}-6 \hat{j}-y \hat{k} \quad\) may be parallel

1 \(x=0, y=\frac{2}{3}\)
2 \(x=\frac{-36}{5}, y=\frac{5}{3}\)
3 \(x=\frac{-15}{3}, y=\frac{23}{5}\)
4 \(x=\frac{36}{3}, y=\frac{15}{14}\)
VECTORS

268997 The unit vector perpendicular to \(\vec{A}=2 \hat{i}+3 \hat{j}+\hat{k}\) and \(\vec{B}=\hat{i}-\hat{j}+\hat{k}\) is

1 \(\frac{4 \hat{i}-\hat{j}-5 \hat{k}}{\sqrt{42}}\)
2 \(\frac{4 \hat{i}-\hat{j}+5 \hat{k}}{\sqrt{42}}\)
3 \(\frac{4 \hat{i}+\hat{j}+5 \hat{k}}{\sqrt{42}}\)
4 \(\frac{4 \hat{i}+\hat{j}-5 \hat{k}}{\sqrt{42}}\)
VECTORS

269010 If\(\vec{A}=\frac{1}{\sqrt{2}} \cos \theta \hat{i}+\frac{1}{\sqrt{2}} \sin \theta \hat{j}\), what will be the unit vector perpendicular to \(\vec{A}\)

1 \(\cos \theta \hat{i}+\sin \hat{\theta j}\)
2 \(-\cos \theta \hat{i}+\sin \theta \hat{j}\)
3 \(\frac{\cos \theta \hat{i}+\sin \theta \hat{j}}{\sqrt{2}}\)
4 \(\sin \theta \hat{i}-\cos \hat{\theta j}\)
VECTORS

269011 \((\hat{i}+\hat{j}) \times(\hat{i}-\hat{j})=\)

1 \(-2 \hat{k}\)
2 \(2 \hat{k}\)
3 zero
4 \(2 \hat{i}\)
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