TS EAMCET · Maths · Vector Algebra
\(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are three vectors such that \(|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{c}|=3 \quad\) and \(\mathbf{b}, \mathbf{c} \quad\) are perpendicular. If projection of \(\mathbf{b}\) on \(\mathbf{a}\) is the same as the projection of \(\mathbf{c}\) on \(\mathbf{a}\), then \(|\mathbf{a}-\mathbf{b}+\mathbf{c}|\) is equal to
- A \(\sqrt{2}\)
- B \(\sqrt{7}\)
- C \(\sqrt{14}\)
- D \(\sqrt{21}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{14}\)
Step-by-step Solution
Detailed explanation
Given that, \(|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{c}|=3\) \(\because b\) and \(c\) are perpendicular. \(\therefore \mathrm{b} \cdot \mathrm{c}=0\) And projection of \(b\) on \(a=\frac{a \cdot b}{|\mathbf{a}|}\) Projection of \(\mathbf{c}\) on…
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
- The solution of the differential equation satisfying when , isTS EAMCET 2019 Easy
- If one of the lines in the pair of straight line given by \(4 x^2+6 x y+k y^2=0\) bisects the angle between the coordinate axes, then \(k \in\)TS EAMCET 2011 Medium
- If \((-c, c)\) is the set of all values of \(x\) for which the expansion of \((7-5 x)^{-2 / 3}\) is valid, then \(5 c+7=\)TS EAMCET 2023 Medium
- \(\cos \alpha \sin (\beta-\gamma)+\cos \beta \sin (\gamma-\alpha)\) \(+\cos \gamma \sin (\alpha-\beta)\) is equal toTS EAMCET 2003 Medium
- The point \(P(1,4)\) occupies the positions \(A, B\) and \(C\) respectively after undergoing the following three transformation successively. I. Reflection about the line \(y=x\). II. Translation through a distance of 1 unit along the positive direction of \(X\)-axis. III. Rotation of the line \(O B\) through an angle \(\frac{\pi}{4}\) about the origin in the anti-clockwise direction. Then, the coordinates of \(C\) areTS EAMCET 2019 Easy
- If \(\alpha\) and \(\beta\) are the roots of \(x^2-2 x+4=0\), then the value of \(\alpha^6+\beta^6\) isTS EAMCET 2009 Medium
More PYQs from TS EAMCET
- A small block of mass is placed on a horizontal slab at a height of above the floor. The block is pressed against a horizontal spring fixed at one end to compress the spring through Upon releasing, the block moves horizontally till it leaves the spring. Calculate the horizontal distance covered by the block after leaving the slab and just before hitting the ground. The spring constant is
(Assume ).TS EAMCET 2021 Medium - Among the following statements, the correct statement for a wave isTS EAMCET 2023 Easy
- One third litre of \(x \mathrm{MK}_2 \mathrm{Cr}_2 \mathrm{O}_7\) is required to completely oxidise \(2 \mathrm{~L}\) of \(0.1 \mathrm{M}\) ferrous ammonium sulphate in acid medium. What Is \(x\) ?TS EAMCET 2019 Medium
- If \(y=e^{a x}(\cos b x+\sin b x)\) satisfies the equation \(\frac{d^2 y}{d x^2}-K \frac{d y}{d x}+L y=0\), then \(L+b K=\)TS EAMCET 2020 Easy
- If \(\bar{a}=\bar{i}-2 \bar{j}+2 \bar{k}, \bar{b}=6 \bar{i}+3 \bar{j}-2 \bar{k}, \bar{c}=-4 \bar{i}+3 \bar{j}+12 \bar{k}\) are three vectors then \(\sqrt{(|\bar{a}|+|\bar{b}|+|\bar{c}|)+|\bar{a}+\bar{b}+\bar{c}|}=\)TS EAMCET 2025 Medium
- A pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in first throw and composite numbers on both the dice in second throw isTS EAMCET 2022 Medium