MHT-CET Vectors — practice questions
30 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MHT-CET Vectors in the app →Which of the following is a **vector** quantity?The magnitude of the zero (null) vector $\vec 0$ is:A unit vector along a non-zero vector $\vec a$ is given by:$\overrightarrow{PQ} + \overrightarrow{QR}$ equals (triangle law of addition):The magnitude of the vector $\vec a = 4\hat i + 0\hat j + 3\hat k$ is:The position vector of the **midpoint** of the segment joining points with position vectors $\vec a$ and $\vecThe triangle inequality for vectors states:If $\vec{PQ} = \vec a$, then $\vec{QP}$ equals:The position vector of the **centroid** of triangle with vertices $A(\vec a),\ B(\vec b),\ C(\vec c)$ is:Two non-zero vectors $\vec a$ and $\vec b$ are **collinear** (parallel) if and only if there exists a non-zeroIn the **parallelogram law** of vector addition, if $\vec a$ and $\vec b$ act along two adjacent sides $\overrVector $\vec a$ is directed due north with $|\vec a| = 24$ and vector $\vec b$ is directed due west with $|\veThe distance from the point $P(2, 3, 4)$ to the **x-axis** is:Point $R$ divides the line segment joining $A(\vec a)$ and $B(\vec b)$ **internally** in the ratio $m : n$. ThThe point dividing the line segment joining $A(2, -6, 8)$ and $B(-1, 3, -4)$ internally in ratio $1:3$ has cooIf $\vec a = 4\hat i + 3\hat k$ and $\vec b = -2\hat i + \hat j + 5\hat k$, then $2\vec a + 5\vec b$ equals:Vectors $\vec a = \hat i - 2\hat j + 3\hat k$ and $\vec b = 3\hat i - 6\hat j + 9\hat k$ are:If three points $A(\vec a), B(\vec b), C(\vec c)$ are **collinear**, then $\overrightarrow{AC}$ must equal:The position vector of the centroid of the **tetrahedron** with vertices $A(\vec a), B(\vec b), C(\vec c), D(\If vectors $2\hat i - q\hat j + 3\hat k$ and $4\hat i - 5\hat j + 6\hat k$ are collinear, then $q$ equals:Vector $\vec{AB} = 2\hat i - 4\hat j + 7\hat k$ has initial point $A(1, 5, 0)$. The terminal point $B$ has cooFind a unit vector in the direction of $\vec a = \hat i - 2\hat j$:Find the value of $\lambda$ and $\mu$ if the non-zero, non-collinear vectors $\vec a$ and $\vec b$ satisfy $\vVector $4\hat i + 13\hat j - 18\hat k$ expressed as a linear combination of $\hat i - 2\hat j + 3\hat k$ and $If $\vec a, \vec b, \vec c$ are the position vectors of $A, B, C$ and $5\vec a - 3\vec b - 2\vec c = \vec 0$, If $G(a, 2, -1)$ is the centroid of the triangle with vertices $P(1, 3, 2),\ Q(3, b, -4),\ R(5, 1, c)$, then $The centroid of the tetrahedron with vertices $A(3, -5, 7),\ B(5, 4, 2),\ C(7, -7, -3),\ D(1, 0, 2)$ is:If $A(0, 3, 0), B(0, 0, 4), C(0, 3, 4)$ are vertices of a triangle, the position vector of its **incentre** isPoints $A(3, 2, p), B(q, 8, -10), C(-2, -3, 1)$ are collinear. The values of $p$ and $q$ are:Are the four points $A(1, -1, 1), B(-1, 1, 1), C(1, 1, 1), D(2, -3, 4)$ coplanar?