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The dot products of a vector with the vectors \( \hat i - 3\hat k, \hat i - 2\hat k \) and \( \hat i + \hat j + 4\hat k\) are 0,5 and 8 respectively. Find the vector.
cbse
class12
modelpaper
2012
sec-b
q20
math
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asked
Feb 3, 2013
by
thanvigandhi_1
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The scalar product of the vector \( \hat i + 2\hat j + 4\hat k \) with a unit vector along the sum of vectors \( \hat i + 2\hat j + 3\hat k \) and \( \lambda \hat i + 4\hat j - 5\hat k \) is equal to one. Find the value of \( \lambda \).
cbse
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2012
sec-b
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Feb 4, 2013
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thanvigandhi_1
0
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Find a vector in the direction of vectors \( 5\hat i - \hat j + 2\hat k\) which has magnitude 8 units.
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2012
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Feb 4, 2013
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Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \( \hat i +2\hat j - \hat k \: and \: -\hat i + \hat j + \hat k\) respectively in the ratio 2 : 1 (i) internally (ii) externally
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2012
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Jan 14, 2013
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Find a vector of magnitude 15 which is perpendicular to both the vectors \( 4\hat i - \hat j + 8\hat k \) and \( - \hat j + \hat k\)
cbse
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modelpaper
2012
sec-b
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math
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Jan 27, 2013
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Let \( \overrightarrow a = 2\hat i + \hat k, \overrightarrow b = \hat i + \hat j + \hat k\) and \( \overrightarrow c = 4\hat i - 3\hat j + 7\hat k\) be three vectors. Find a vector \( \overrightarrow r \) which satisfies \( \overrightarrow r\) x \( \overrightarrow b = \overrightarrow c \) x \( \overrightarrow b\) and \( \overrightarrow r. \overrightarrow a =0.\)
cbse
class12
modelpaper
2012
sec-b
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asked
Jan 17, 2013
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thanvigandhi_1
0
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Show that the points A, B and C with position vectors \( \overrightarrow a = 3\hat i - 4\hat j - 4\hat k, \overrightarrow b = 2\hat i - \hat j + 4\hat k \: and \: \overrightarrow c = \hat i - 3\hat j - 5\hat k,\) respectively, form the vertices of a right angled triangle.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Find a unit vector perpendicular to each of the vectors \( \overrightarrow a+\overrightarrow b \: and \: \overrightarrow a-\overrightarrow b\), where \( \overrightarrow a=3\hat i+2\hat j +2 \hat k \) and \( \overrightarrow b = \hat i + 2\hat j -2\hat k.\)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Feb 4, 2013
by
thanvigandhi_1
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