JEE Advanced Vectors & 3D Geometry — practice questions
101 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Vectors & 3D Geometry in the app →Question 7: If the angle between vectors A and B is $\theta$, then the value of the product $(B\times A).A$ isQuestion 6: If the scalar and vector products of two vectors A and B are equal in magnitude, then the angle beThe projection of vector $\vec A$ on vector $\vec B$ is given byWhich statement correctly compares the dot product and cross product?If the angle between vectors $\vec A$ and $\vec B$ is $90^\circ$, thenWhich statement about a null vector is correct?When subtracting vectors, $\vec A-\vec B$ is evaluated asAccording to the parallelogram law shown, the diagonal through the common initial point represents
$ in 3D, the magnitude of the position vector $\overrightarrow{OP}$ is
$, then its position vector from the origin is
$Which identity for the scalar triple product is correct?If $\mathbf{A}\cdot\mathbf{B}=0$, then the vectors $\mathbf{A}$ and $\mathbf{B}$ areWhich of the following equals $\mathbf{A}\times\mathbf{B}$ for $\mathbf{A}=\langle 1,2,0\rangle$ and $\mathbf{For vectors $\mathbf{A}=\langle 2,-1,3\rangle$ and $\mathbf{B}=\langle 4,0,-2\rangle$, the dot product $\mathbIf $\mathbf{A}=\langle 1,2,3\rangle$, then $3\mathbf{A}$ equalsThe position vector of a point $P(x,y,z)$ in three-dimensional space is given byIf $\mathbf{A}=\langle 2,-1,4\rangle$ and $\mathbf{B}=\langle 3,5,-2\rangle$, then $\mathbf{A}+\mathbf{B}$ is$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $$\cos 2\theta$ equals:If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals:A student claims that the perpendicular distance from a point to a line equals the magnitude of the projectionIf a point $\bar r$ lies on the line joining position vectors $\bar a$ and $\bar b$, then in the representatioWhich statement best distinguishes direction ratios from direction cosines for a line in three dimensions?Suppose a line is written as $\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}$. Which of the following is aFor a line with vector equation $\bar r=\bar a+\lambda\bar b$, which statement is correct?If $(d,m,n)$ are direction cosines of a line, which relation must hold?Let $P(a,b,c)$ be a point and let a line pass through $(x_1,y_1,z_1)$ with direction ratios $(d,m,n)$. If $\veThe symmetric equation of the line passing through $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ isWhich non-parametric vector condition represents the line through points with position vectors $\bar a$ and $\If a line passes through points with position vectors $\bar a$ and $\bar b$, then its vector equation isWhich non-parametric vector equation represents the line passing through the point with position vector $\bar The vector equation of the line passing through the point with position vector $\bar a$ and parallel to the veIf a point on the line $\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}=\lambda$, then its coordinates areA line passes through the point $(x_1,y_1,z_1)$ and has direction ratios $(a,b,c)$. Which of the following is sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:sin(A + B) equals:cos(A + B) equals:sin(60°) cos(30°) + cos(60°) sin(30°) equals:If sin θ = 3/5 (θ in Q1), find cos θ:Find cos(75°) using cos(A + B):sin(2θ) equals:cos(2θ) equals:Find sin(15°):If tan θ = 1/2 (acute), find sin 2θ:For 0 ≤ θ < 2π, solutions of sin θ = 1/2:1 - cos²θ equals:sin(A) + sin(B) equals (sum-to-product):In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:tan(A + B) equals:sin(180° - θ) equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:If sin θ + cos θ = 1, then sin θ × cos θ equals:General solution of cos θ = 0:If tan θ + cot θ = 2, find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Minimum value of sin²θ + cos⁴θ:If sin θ = 12/13 (acute), find tan(θ/2):In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):General solution of sin θ = sin α:The angle $\theta$ between two planes with normal vectors $\vec{n}_1$ and $\vec{n}_2$ satisfiesA line passes through the point $(x_1,y_1,z_1)$ and is parallel to the vector $\langle a,b,c\rangle$. Its symmIf $(2,-3,6)$ are direction ratios of a line, then a set of direction cosines isIf $(l,m,n)$ are the direction cosines of a line, then which relation must hold?If $vec{a}$, $vec{b}$ and $vec{c}$ are coplanar, then the scalar triple product satisfiesThe projection of vector $vec{a}$ on vector $vec{b}$ isIf $vec{a}$ and $vec{b}$ are non-zero vectors making an angle $theta$, then $vec{a} \cdot vec{b}$ isThe distance between $(1, 2, 3)$ and $(4, 6, 3)$ in 3D is:The direction cosines of a line with direction ratios $(2, -1, 2)$ are:The plane $2x - y + 3z + 5 = 0$ has normal vector:The distance from $(1, 1, 1)$ to the plane $2x + 2y + z + 3 = 0$ is:The magnitude of the vector $\vec a = 3\hat i + 4\hat j$ is:The dot product $\vec a\cdot\vec b$ of $\vec a = 2\hat i - \hat j + 3\hat k$ and $\vec b = \hat i + 4\hat j + The cross product $\vec a\times\vec b$ of two parallel non-zero vectors is:Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:If a = 2i + 3j + k and b = i − j + 2k, then a · b equals:Two non-zero vectors a and b are PERPENDICULAR if and only if:A UNIT VECTOR in the direction of v = 3i + 4j is:The scalar triple product [a b c] geometrically represents:The vector triple product a × (b × c) simplifies via:The Cartesian equation of a plane with intercepts 2, 3, 6 on the x, y, z axes is:For direction cosines l, m, n of any line in 3D:A point R divides the line joining P (position vector a) and Q (position vector b) INTERNALLY in the ratio m:nThe angle θ between two PLANES with normals n1 and n2 satisfies: