COMEDK · Maths · 33. Vector Algebra
If the area of the parallelogram with \(\mathbf{a}\) and \(\mathbf{b}\) as two adjacent sides is 15 sq units, then the area of the parallelogram having \(3 \mathbf{a}+2 \mathbf{b}\) and \(\mathbf{a}+3 \mathbf{b}\) as two adjacent sides in sq units is
- A 45
- B 75
- C 105
- D 120
Answer & Solution
Correct Answer
(C) 105
Step-by-step Solution
Detailed explanation
We know that, if \(\mathbf{a}\) and \(\mathbf{b}\) are two adjacent sides of a parallelogram, then Area \(=|a \times b|=15\) (given) ...(i) If the sides are \((3 \mathbf{a}+2 \mathbf{b})\) and \((\mathbf{a}+3 \mathbf{b})\) Then, area of parallelogram…
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
- A line making angles \(45^{\circ}\) and \(60^{\circ}\) with the positive directions of the axis of \(X\) and \(Y\), makes with the positive direction of \(Z\)-axis, an angle ofCOMEDK 2015 Easy
- The focus of the parabola isCOMEDK 2020 Easy
- If \(3 x^{2}+x y-y^{2}-3 x+6 y+k=0\) represents a pair of lines, then \(k=\)COMEDK 2019 Easy
- In a \(\triangle A B C, \operatorname{cosec} A(\sin B \cos C+\cos B \sin C)=\)COMEDK 2015 Easy
- If a polygon of \(n\) sides has 275 diagonals, then \(n\) is equal toCOMEDK 2021 Easy
- The magnitude of the projection of the vector \(-\hat{\imath}+2 \hat{\jmath}-\hat{k}\) on the z -axis isCOMEDK 2025 Easy
More PYQs from COMEDK
- The sum of the degree and order of the following differential equation \(\left[1-\left(\dfrac{d y}{d x}\right)^2\right]^{\dfrac{3}{2}}=k x \dfrac{d^2 y}{d x^2}\)COMEDK 2023 Easy
- If \(x=2 a \sin ^{-1}\left(\sqrt{\dfrac{y}{2 a}}\right)-\sqrt{2 a y-y^2}\) then \(\dfrac{d y}{d x}=\)COMEDK 2025 Medium
- A \(5.80 \mu \mathrm{~F}\) parallel plate air capacitor has a plate separation of 5 mm and is charged to a potential difference of 400 V . The energy density in the region between the plates isCOMEDK 2024 Medium
- What volume of \(0.2 \mathrm{M} \mathrm{CH}_3 \mathrm{COOH}\) needs to be added to \(100 \mathrm{ml}\) of \(0.4 \mathrm{M} \mathrm{CH}_3 \mathrm{COONa}^2\) solution to prepare a buffer of pH equal to 4.91 ? (\(\mathrm{pK}_{\mathrm{a}}\) of \(\mathrm{CH}_3 \mathrm{COOH}\) is 4.76)COMEDK 2025 Medium
- \(\text { The general solution of the differential equation } \dfrac{d y}{d x}=\dfrac{x y}{x^2+y^2} \text { is }\)COMEDK 2024 Medium
- Two bodies of masses \(1 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) have equal momentum, then the ratio of their kinetic energies isCOMEDK 2013 Easy