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A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector \(3\hat{i}+15\hat{j}+6\hat{k}\) and the other is along the vector \(2\hat{i}+10\hat{j}+\lambda\hat{k}\), then the value of \(\lambda\) is :

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) for any two vectors, then vectors \(\vec{a}\) and \(\vec{b}\) are:

Let \(\theta\) be the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) such that \(\sin\theta=\frac{3}{5}\). Then, \(\hat{a} \cdot \hat{b}\) is equal to:

The vector with terminal point \(A(2,-3,5)\) and initial point \(B(3, 4, 7)\) is:

For any two vectors \(\vec{a}\) and \(\vec{b}\), which of the following statements is always true?

The unit vector perpendicular to both vectors \(\hat{i}+\hat{k}\) and \(\hat{i}-\hat{k}\) is:

If \(\vec{a}=2\hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}-\hat{k}\), then \(\vec{a}\) and \(\vec{b}\):

If \(|\vec{a}|= 2\) and \(-3\le k\le2\), then \(|\vec{k}\vec{a}|\in\):

If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(|\vec{a}|=1,|\vec{b}|=2~and\vec{a}\cdot\vec{b}=\sqrt{3}\) then the angle between \(2\vec{a}\) and \(-\vec{b}\) is:

The vectors \(\vec{a}=2\hat{i}-\hat{j}+\hat{k}\), \(\vec{b}=\hat{i}-3\hat{j}-5\hat{k}\) and \(\vec{c}=-3\hat{i}+4\hat{j}+4\hat{k}\) represents the sides of

Let \(\vec{a}\) be any vector such that \(|\vec{a}|=a\) The value of \(|\vec{a}\times\hat{i}|^{2}+|\vec{a}\times\hat{j}|^{2}+|\vec{a}\times\hat{k}|^{2}\) is:

The position vectors of points P and Q are \(\vec{p}\) and \(\vec{q}\) respectively. The point R divides line segment PQ in the ratio 3:1 and S is the mid-point of line segment PR. The position vector of S is: