List of top Mathematics Questions on Addition of Vectors

Given vectors $\vec{a}, \vec{b}, \vec{c}$ are non-collinear and $(\vec{a}+\vec{b})$ is collinear with $(\vec{b}+\vec{c})$ which is collinear with $\vec{a}$, and $|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}$, find $|\vec{a}+\vec{b}+\vec{c}|$.

If $|\mathbf{a}| = \sqrt{3}, |\mathbf{b}| = 5, |\mathbf{b}||\mathbf{c}| = 10$, the angle between $\mathbf{b}$ and $\mathbf{c}$ is $\pi/3$, and $\mathbf{a}$ is perpendicular to $\mathbf{b} \times \mathbf{c}$, then the value of $|\mathbf{a} \times (\mathbf{b} \times \mathbf{c})|$ is:

The sides of a triangle are $\sin\alpha$, $\cos\alpha$, and $\sqrt{1+\sin\alpha\cos\alpha}$ for some $0 < \alpha < \frac{\pi}{2}$. Then, the greatest angle of the triangle is:

If the vectors $\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}$, $\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}$ and $\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}$ are coplanar and the projection of $\overrightarrow{a}$ on the vector $\overrightarrow{b}$ is $\sqrt{54}$ units, then the sum of all possible values of $\lambda + \mu$ is equal to

If the points with position vectors $a\hat{i} +10\hat{j} +13\hat{k}, 6\hat{i} +11\hat{k} +11\hat{k},\frac{9}{2}\hat{i}+B\hat{j}−8\hat{k}$ are collinear, then (19α-6β)² is equal to

Let $\vec{a} = 6\hat{i} + 9\hat{j} + 12\hat{k}$, $\vec{b} = a\hat{i} + 11\hat{j} - 2\hat{k}$, and $\vec{c}$ be vectors such that $\vec{a} \times \vec{c} = \vec{a} \times \vec{b}$. If $\vec{a} \cdot \vec{c} = -12$ and $\vec{c} \cdot (\hat{i} - 2\hat{j} + \hat{k}) = 5$, then $\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k})$ is equal to:

Let the vectors $\mathbf{u}_1 = \hat{i} + \hat{j} + a\hat{k}, \mathbf{u}_2 = \hat{i} + b\hat{j} + \hat{k}$, and $\mathbf{u}_3 = c\hat{i} + \hat{j} + \hat{k}$ be coplanar. If the vectors $\mathbf{v}_1 = (a + b)\hat{i} + c\hat{j} + c\hat{k}, \mathbf{v}_2 = a\hat{i} + (b + c)\hat{j} + a\hat{k}, \mathbf{v}_3 = b\hat{i} + b\hat{j} + (c + a)\hat{k}$ are also coplanar, then $6(a + b + c)$ is equal to:

Let O be the origin and the position vector of the point P be $\hat i-2\hat j+3\hat k$. If the position vectors of the points A, B and C are $-2\hat i+\hat j-3\hat k,2\hat i+4\hat j-2\hat k$ and $-4\hat i+2\hat j-\hat k$ respectively then the projection of the vector $\overrightarrow{OP}$ on a vector perpendicular to the vectors $\overrightarrow{ AB}$ and $\overrightarrow {AC}$ is

Let S be the set of all (λ, μ) for which the vectors $ λ {i}ˆ-jˆ+kˆ, iˆ +2jˆ+µkˆ and 3iˆ -4jˆ +5kˆ, where λ-μ = 5, are coplanar, then $$ \sum_{(λ, μ) εs}80(λ^2, μ^2) $ is equal to

Let f(x)=$\left\{\begin{matrix} |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\ |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.$ where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable is

A parallelogram is constructed on vectors $\vec{a}=3\vec{\alpha}-\vec{\beta},\; \vec{b}=\vec{\alpha}+3\vec{\beta}$. If $|\vec{\alpha}|=|\vec{\beta}|=2$ and angle between them is $\pi/3$, find length of a diagonal

Let a, b, c be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then | a+ b+ c| in terms of θ is equal to

With respect to a rectangular Cartesian coordinate system, three vectors are expressed as a = 4 i- j, b=-3 i+2 j and c=- k. The unit vector along the direction of sum of these vectors is

The vector sum of two forces is perpendicular to their vector differences. In that case the forces