TS EAMCET · Maths · Vector Algebra
If \(2 \hat{i}+3 \hat{j}-4 \hat{k}\) and \(-\hat{i}+2 \hat{j}+\hat{k}\) are the two diagonals of a parallelogram, then the area of the parallelogram in square units is
- A \(\frac{1}{2} \sqrt{170}\)
- B \(\sqrt{174}\)
- C \(\sqrt{\frac{87}{2}}\)
- D \(\frac{1}{4} \sqrt{174}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{87}{2}}\)
Step-by-step Solution
Detailed explanation
Let \(\overrightarrow{\mathrm{d}}_1=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{d}}_2=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) Now Area is \(=\frac{1}{2} \overline{\mathrm{d}}_1 \times \overline{\mathrm{d}}_2\)…
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
- If \(6 x-x^2+12\) attains its extreme value \(\beta\) at \(x=\alpha\) then \(\beta=\)TS EAMCET 2022 Easy
- If \(f: R \rightarrow R\) is defined by \(f(x)=x-[x]\), where \([x]\) is the greatest integer not exceeding \(x\), then the set of discontinuous of \(f\) isTS EAMCET 2002 Medium
- The area of the quadrilateral formed by the lines \(x+2 y+3=0,2 x+4 y+9=0\), \(x-2 y+3=0\) and \(3 x-6 y+11=0\) isTS EAMCET 2025 Medium
- \(\begin{aligned} & \frac{1}{x(x+1)(x+2) \ldots(x+n)}=\frac{A_0}{x}+\frac{A_1}{x+1} \ & +\ldots \frac{A_n}{x+n}, 0 \leq i \leq r \Rightarrow A_r \text { is equal to }\end{aligned}\)TS EAMCET 2012 Hard
- The number of all common roots of the equation \(x^4-10 x^3+37 x^2-60 x+36=0\) and the transformed equation of it obtained by increasing any two distinct roots of it by 1, keeping the other two roots fixed, isTS EAMCET 2025 Hard
- If \(\mathrm{A}=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1\end{array}\right], \mathrm{A}^{-1}=\frac{1}{2}\left[\begin{array}{ccc}1 & -1 & 1 \\ -8 & 6 & 2 y \\ 5 & -3 & 1\end{array}\right]\) then the point \((x, y)\) lies on the curve represented by the equationTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- The molecular formula of the final product of the following synthetic scheme is
TS EAMCET 2021 Medium - 1 mole of a real gas is kept at high pressure of 100 bar at \(300 \mathrm{~K}\). If van der Waals constant \(b\) is \(0.005 \mathrm{~L} / \mathrm{mol}\), what are the values of compressibility factor \(\mathrm{Z}\) of the gas and \(\%\) deviation of volume from ideality? \(\begin{array}{llc} & \mathbf{Z} & \text { \% Deviation } \end{array}\)TS EAMCET 2022 Medium
- A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority isTS EAMCET 2012 Medium
- What is the total number of electrons present in one mole of ethane?TS EAMCET 2020 Easy
- If is continuous at , thenTS EAMCET 2018 Easy
- If \(x=\cos 2 t+\log (\tan t)\) and \(y=2 t+\cot 2 t\), then \(\frac{d y}{d x}=\)TS EAMCET 2024 Easy