List of top Mathematics Questions on Vectors asked in MHT CET

Let \(\overline{OD} = \hat{i}+2\hat{j}+6\hat{k}\), \(\overline{CB} = -3\hat{i}-2\hat{k}\) be the diagonals of the parallelogram OBDC and \(\overline{OA} = \hat{i}+2\hat{j}+3\hat{k}\) be another vector. Then the volume of a parallelopiped determined by vectors \(\overline{OA}\), \(\overline{OB}\), and \(\overline{OC}\) (in cubic units), is

If \(\overset{̄}{a}\), \(\overset{̄}{b}\) and \(\overset{̄}{c}\) are three vectors such that \(|\overset{̄}{a}+\overset{̄}{b}+\overset{̄}{c}| = 1\), \(\overset{̄}{c} = λ(\overset{̄}{a}\times \overset{̄}{b})\) and \(|\overset{̄}{a}| = \frac{1}{\sqrt{3}}\), \(|\overset{̄}{b}| = \frac{1}{\sqrt{2}}\), \(|\overset{̄}{c}| = \frac{1}{\sqrt{6}}\), then the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is

The volume of the tetrahedron whose vertices are A\((-1,2,3)\), B\((3,-2,1)\), C\((p,1,3)\), D\((-1,-2,4)\) is \(\frac{16}{3}\) cubic units then the value of p is

Let O\((0,0)\), A\((-1,2)\) and B\((1,3)\) be the vertices of \(△\)OAB. The bisector of angle O intersects side AB at point D. The value of \(\overset{⃗}{OD}\cdot \overset{⃗}{AB}\) is equal to...

If \(|\overset{⃗}{a}| = 3\), \(|\overset{⃗}{b}| = 4\), \(|\overset{⃗}{c}| = 5\) such that each vector is perpendicular to the sum of the other two, then \(|\overset{⃗}{a}+\overset{⃗}{b}+\overset{⃗}{c}|\) is equal to

If ABCDEF is a regular hexagon and \(\overline{AB}+\overline{AC}+\overline{AD}+\overline{AE}+\overline{AF} = p\overline{AD} = q\overline{AO}\), where O is the center of the hexagon, then the values of \(p\) and \(q\) respectively are

If the vectors $\vec{a} = c (\log_7 x) \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = (\log_7 x) \hat{i} + 3c (\log_7 x) \hat{j} - 4\hat{k}$ make obtuse angle for any x > 0, then c belongs to ______.

If $\vec{a} = \lambda x \hat{i} + y \hat{j} + 4z \hat{k}$, $\vec{b} = x \hat{i} + y \hat{j} + 3y \hat{k}$, and $\vec{c} = -2 \hat{i} - 2z \hat{j} - (\lambda + 1) \hat{k}$ such that $\vec{a} + \vec{b} - \vec{c} = \vec{0}$, then the value of $\lambda$ is ______.

If $\bar{a}, \bar{b}, \bar{c}$ are three vectors such that $|\bar{a}| = 3, |\bar{b}| = 5, |\bar{c}| = 7$ then $|\bar{a} - \bar{b}|^2 + |\bar{b} - \bar{c}|^2 + |\bar{c} - \bar{a}|^2$ does not exceed}

In a game, 3 coins are tossed. A person is paid Rs \( 150 \) if he gets all heads or all tails and he is supposed to pay ₹\( 50 \) if he gets one head or two heads. The amount he can expect to win lose on an average per game in ₹ is

The sum of the degree and order of the differential equation $\sqrt{\frac{d^2y}{dx^2}} = \sqrt[5]{\frac{dy}{dx}} - 5$ is

If $\tan 3\theta = \cot \theta$, then $\theta =$

If $\bar{a}$ and $\bar{b}$ are unit vectors and $\theta$ is the angle between them, then $\bar{a} + \bar{b}$ is a unit vector when $\theta$ is

If \(\bar{a}, \bar{b}, \bar{c}\) are three unit vectors such that \(|\bar{a} + \bar{b}|^2 + |\bar{a} + \bar{c}|^2 = 8\), then \(|\bar{a} + 3\bar{b}|^2 + |\bar{a} + 3\bar{c}|^2 =\)

If $\bar{a}, \bar{b}, \bar{c}$ are three vectors such that $|\bar{a}| = 3, |\bar{b}| = 5, |\bar{c}| = 7$ then $|\bar{a} - \bar{b}|^2 + |\bar{b} - \bar{c}|^2 + |\bar{c} - \bar{a}|^2$ does not exceed}

In a game, 3 coins are tossed. A person is paid Rs \( 150 \) if he gets all heads or all tails and he is supposed to pay ₹\( 50 \) if he gets one head or two heads. The amount he can expect to win lose on an average per game in ₹ is