List of top Mathematics Questions on Vectors asked in KCET

The component of \(\hat{i}\) in the direction of the vector \(\hat{i}+\hat{j}+2\hat{k}\) is

If \(|\vec{a}|=2\) and \(|\vec{b}|=3\) and the angle between \(\)\(\vec{a}\) and \(\vec{b}\) is 120°, then the length of the vector \(|\frac{1\vec{a}}{2}-\frac{1\vec{b}}{3}|^2\) is

If \(|\vec{a}\times\vec{b}|\) + \(|\vec{a}.\vec{b}|^2=36\) and \(|\vec{a}|=3\) then \(|\vec{b}|\) is equal to

If \(\vec{\alpha}=\hat{i}-3\hat{j},\vec{\beta}=\hat{i}+2\hat{j}-\hat{k}\) then express If |a×b|+|a.b|=36 and |a|=3 then |b| is equal to\(\vec{\beta}\) in the form \(\vec{β}=\vec{β_1}+\vec{β_2}\) where \(\vec{β}_1\) is parellel to \(\vec{\alpha}\) and \(\vec{β}_2\) is perpendicular to \(\vec{\alpha}\) then \(\vec{β_1}\) is given by

If the vectors \(2\hat{i}-3\hat{j}+4\hat{k},2\hat{i}+\hat{j}-\hat{k}\) and \(\lambda\hat{i}-\hat{j}+2\hat{k}\) are coplanar, then the value of λ is

The projection of the vector $2\hat{i}+\hat{j}-3\hat{k}$ on the vector $\hat{i}-2\hat{j}-\hat{k}$ is

The vectors \(\overrightarrow {AB}=3\hat i+4\hat k\) and \(\overrightarrow {AC}=5\hat i-2\hat j+4\hat k\) are the sides of a △ABC. The length of the median through A is

The volume of the parallelopiped whose co-terminous edges are \(\hat j+\hat k,\hat i+\hat k\) and \(\hat i+\hat j\) is

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two unit vectors and θ is the angle between them. Then \(\overrightarrow a +\overrightarrow  b\) is a unit vector if

If \(\overrightarrow a,\overrightarrow b,\overrightarrow c\) are three non-coplanar vectors and p,q,r are vectors defined by
\(\overrightarrow p=\frac{\overrightarrow a\times \overrightarrow c}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\) ,\(\overrightarrow q=\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\),\(\overrightarrow r=\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\)then
\((\overrightarrow a+\overrightarrow b).\overrightarrow p+(\overrightarrow b+\overrightarrow c).\overrightarrow q+(\overrightarrow c+\overrightarrow a).\overrightarrow r\) is