List of top Mathematics Questions on Vector basics asked in BITSAT

If \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} - \hat{j} + 2\hat{k} \), then find the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \).
Let a, b, c be three vectors satisfying a × b = ( a × c), | a|=| c|=1, | b|=4 and | b × c|=√(15). If a · b = ?, then λ equals
Let \(\mathbf{a} = \mathbf{i} - \mathbf{k}, \quad \mathbf{b} = x\mathbf{i} + \mathbf{j} + (1-x)\mathbf{k}, \quad \mathbf{c} = y\mathbf{i} + x\mathbf{j} + (1+x-y)\mathbf{k}\). Then \([\mathbf{a}, \mathbf{b}, \mathbf{c}]\) depends on:
The projection of the line joining (3,4,5) and (4,6,3) on the line joining (-1,2,4) and (1,0,5) is:
If i+ j, j+ k, i+ k are position vectors of vertices of triangle ABC taken in order, then ∠ A is equal to:
Let \(\vec a,\vec b,\vec c\) be three vectors satisfying \(\vec a\times\vec b=\vec a\times\vec c\), \(|\vec a|=|\vec c|=1\), \(|\vec b|=4\) and \(|\vec b\times\vec c|=\sqrt{15}\). If \(\vec b-2\vec c=\lambda \vec a\), then \(\lambda\) equals
If the middle points of sides BC, CA and AB of triangle ABC are respectively D, E, F. If the position vectors of A, B, C are \(\hat{i}+\hat{j},\;\hat{j}+\hat{k},\;\hat{k}+\hat{i}\) respectively, then the position vector of the centre of triangle DEF is
If the midpoints of sides BC, CA, AB of triangle ABC are respectively D, E, F, then position vector of centre of triangle DEF, when position vectors of A, B, C are respectively i+ j, j+ k, k+ i, is