Mathematics Tes...

Find the direction ratios of the line 2x = 3y = 5 - 4z ?

If \(\vec{a} = 4\hat{j}\) and \(\vec{b} = 3\hat{j} + 4\hat{k}\), then the vector form of the component of \(\vec{a}\) along \(\vec{b}\) is

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 \(\overrightarrow {{\rm{b}}} \)?

In what ratio is the line joining the points A (- 1, 1) and B (5, 7) divided by the line x + y = 4?

If the direction cosines of a line are (1/k, 2/k, -2/k) then k is

If \(\vec a\) and \(\vec b\) represent the sides AB and BC of a regular hexagon ABCDEF, then \(\vec {FA}\) is equal to

Find a unit vector in the direction of \(\overrightarrow {AB} \), where A (1, 2, 3) and B (4, 5, 6) are the given points ?

Find the angle between the planes 2x - 3y + 4z = 1 and - x + y = 4 ?

If the two lines  \(\frac{x-t}{2}=\frac{y-4}{3}=\frac{z-5}{4}\) and \(\frac{x}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) are intersecting then; what will be the value of t?

If \(\vec a + \vec b + \vec c = \vec 0,\;|\vec a| = 3,\;|\vec b| = 5\) and \(|\vec c| = 7\), find the angle between \(\vec a\) and \(\vec b\).