Mathematics Test

If \(\overrightarrow {{\rm{a}}} \) and \(\overrightarrow {{\rm{b}}} \) are vectors such that \(\overrightarrow {|{\rm{a|}}} { = 2,{\rm{\;}}\overrightarrow {|{\rm{b}|}} }= 7\) and \(\overrightarrow {{\rm{a\;}}} \times {\rm{\;\vec b}} = 3{\rm{\hat i}} + 2{\rm{\hat j}} + 6{\rm{\hat k}},\) then what is the acute angle between \(\overrightarrow {{\rm{a}}} \) and \(\overrightarrow {{\rm{b}}} \)?

Question 1/10

<2, 3, 5>

<6, 4, - 3>

<2, 3, - 4>

None of these

Question 2/10

\(\dfrac{12}{10\sqrt{3}}(3\hat{j}+4\hat{k})\)

\(\rm \dfrac {12}{25}(3\vec j + 4 \vec k)\)

\(\dfrac{12}{\sqrt{13}}(3\hat{j}+4\hat{k})\)

\((3\hat{j}+4\hat{k})\)

Question 3/10

30°

45°

60°

90°

Question 4/10

3 : 1

1 : 2

4 : 3

None of these

Question 5/10

± (1/√3)

1/3

±√3

± 3

Question 6/10

\(\vec b - \vec a\)

\(\vec a - \vec b\)

\( \vec a+\vec b \)

None of these

Question 7/10

\(\frac{1}{{\sqrt 3 }}\;\hat i - \frac{1}{{\sqrt 3 }}\;\hat j + \frac{1}{{\sqrt 3 }}\;\hat k\)

\(\frac{1}{{\sqrt 3 }}\;\hat i + \frac{1}{{\sqrt 3 }}\;\hat j + \frac{1}{{\sqrt 3 }}\;\hat k\)

\(\frac{1}{{\sqrt 3 }}\;\hat i + \frac{1}{{\sqrt 3 }}\;\hat j - \frac{1}{{\sqrt 3 }}\;\hat k\)

\(\frac{1}{{\sqrt 3 }}\;\hat i - \frac{1}{{\sqrt 3 }}\;\hat j - \frac{1}{{\sqrt 3 }}\;\hat k\)

Question 8/10

\({\cos ^{ - 1}}\left( {\frac{3}{{\sqrt {58} }}} \right)\)

\({\cos ^{ - 1}}\left( {\frac{5}{{\sqrt {58} }}} \right)\)

\({\cos ^{ - 1}}\left( {\frac{7}{{\sqrt {58} }}} \right)\)

\({\cos ^{ - 1}}\left( {\frac{1}{{\sqrt {58} }}} \right)\)

Question 9/10

1

7

-1

0

Question 10/10

π / 2

π / 3

π / 6

π / 4