JEE Mains · Maths · STD 12 - 10. vector algebra
The area of the quadrilateral \(ABCD\) with vertices \(A (2,1,1), B (1,2,5), C (-2,-3,5)\) and \(D (1,-6,-\) 7) is equal to
- A \(48\)
- B \(8 \sqrt{38}\)
- C \(54\)
- D \(9 \sqrt{38}\)
Answer & Solution
Correct Answer
(B) \(8 \sqrt{38}\)
Step-by-step Solution
Detailed explanation
\(\text { Vector Area }=\overrightarrow{ v }\) \(=\frac{1}{2} \overrightarrow{ AB } \times \overrightarrow{ AC }+\frac{1}{2} \overrightarrow{ AC } \times \overrightarrow{ AD }\) \(=\frac{1}{2}(\overrightarrow{ AB }-\overrightarrow{ AD }) \times \overrightarrow{ AC }\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let the normal at the point \(P\) on the parabola \(y ^{2}=\) \(6 x\) pass through the point \((5,-8)\). If the tangent at \(P\) to the parabola intersects its directrix at the point \(Q\), then the ordinate of the point \(Q\) isJEE Mains 2022 Medium
- If the sum and product of four positive consecutive terms of a \(G.P.\), are \(126\) and \(1296\), respectively, then the sum of common ratios of all such \(GPs\) is \(.........\).JEE Mains 2023 Hard
- If the equation of the plane containing the line \(x+2 y+3 z-4=0=2 x+y-z+5\) and perpendicular to the plane \(\overrightarrow{ r }=(\hat{ i }-\hat{ j })+\lambda(\hat{ i }+\hat{ j }+\hat{ k })+\mu(\hat{ i }-2 \hat{ j }+3 k )\) \(a x+b y+c z=4\), then \((a-b+c)\) is equal toJEE Mains 2023 Hard
- The tangents at the point \(A (1,3)\) and \(B (1,-1)\) on the parabola \(y ^{2}-2 x -2 y =1\) meet at the point \(P\). Then the area (in unit \({ }^{2}\) ) of the triangle \(PAB\) is :-JEE Mains 2022 Hard
- The locus of mid-points of the line segments joining \((-3,-5)\) and the points on the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) is :JEE Mains 2021 Hard
- If \(5x + 9 = 0\) is the directrix of the hyperbola \(16x^2 -9y^2 = 144,\) then its corresponding focus isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The number of solutions, of the equation \(\mathrm{e}^{\sin x}-2 e^{-\sin x}=2\) isJEE Mains 2024 Hard
- Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is reciprocal to that of the hyperbola \(2 x^2-2 y^2=1\). If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is \(................\).JEE Mains 2023 Hard
- If the projection of the vector \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) on the sum of the two vectors \(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}\) and \(-\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is \(1,\) then \(\lambda\) is equal to ..... .JEE Mains 2021 Medium
- Let \(A\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right] .\) If \(A^{-1}=\alpha I+\beta A, \alpha, \beta \in R, I\) is a \(2 \times 2\) identity matrix, then \(4(\alpha-\beta)\) is equal to:JEE Mains 2021 Medium
- Consider the region \(R=\left\{(x, y): x \leq y \leq 9-\frac{11}{3} x^2, x \geq 0\right\}\).
The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:JEE Mains 2025 Hard - If \(\alpha\) and \(\beta\) are the roots of the equation \(2 z^2-3 z-2 \mathrm{i}=0\), where \(\mathrm{i}=\sqrt{-1}\), then \(16 \cdot \operatorname{Re}\left(\frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}}\right) \cdot \operatorname{lm}\left(\frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}}\right)\) is equal toJEE Mains 2025 Hard