MHT CET · Maths · Vector Algebra
\(\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}-2 \hat{j}+3 \hat{k}, \bar{c}=\hat{i}-2 \hat{j}+\hat{k}\), then \(a\) vector of magnitude 6 units, which is parallel to the vector \(2 \bar{a}-\bar{b}+3 c\), is
- A \(2 \hat{i}-4 \hat{j}+4 \hat{k}\)
- B \(\hat{i}-\hat{j}+2 \hat{k}\)
- C \(4 \hat{i}+4 \hat{j}-2 \hat{k}\)
- D \(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\)
Answer & Solution
Correct Answer
(A) \(2 \hat{i}-4 \hat{j}+4 \hat{k}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \overline{\mathrm{a}}-\overline{\mathrm{b}}+3 \overline{\mathrm{c}} \\
= & (2-4+3) \hat{\mathrm{i}}+(2+2-6) \hat{\mathrm{j}}+(2-3+3) \hat{\mathrm{k}} \\
= & \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}
\end{aligned}\)
\(\therefore \quad\) Required vector is the multiple of the above vector and has magnitude 6 units.
Option (A) satisfies this condition.
& \overline{\mathrm{a}}-\overline{\mathrm{b}}+3 \overline{\mathrm{c}} \\
= & (2-4+3) \hat{\mathrm{i}}+(2+2-6) \hat{\mathrm{j}}+(2-3+3) \hat{\mathrm{k}} \\
= & \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}
\end{aligned}\)
\(\therefore \quad\) Required vector is the multiple of the above vector and has magnitude 6 units.
Option (A) satisfies this condition.
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 one end of the diameter is \((1,1)\) and the other end lies on the line \(x+y=3\), then locus of centre of circle isMHT CET 2008 Medium
- Two lines \(\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1} \quad\) and \(\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4} \quad\) intersect at the point \(\mathrm{R}\). Then reflection of \(\mathrm{R}\) in the \(x y\)-plane has co-ordinatesMHT CET 2023 Medium
- The value of \(\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)\) isMHT CET 2023 Easy
- If \(\mathrm{F}(x)=\left(\mathrm{f}\left(\frac{x}{2}\right)\right)^2+\left(\mathrm{g}\left(\frac{x}{2}\right)\right)^2\), where \(\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x)\) and \(g(x)=\mathrm{f}^{\prime}(x)\) and given by \(\mathrm{F}(5)=5\), then \(\mathrm{F}(10)\) is equal toMHT CET 2024 Medium
- If \(\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha\), where \(-1 \leq x \leq 1\), \(-3 \leq y \leq 3, x \leq \frac{y}{3}\), then for all \(x, y\) \(9 x^2-6 x y \cos \alpha+y^2\) is equal toMHT CET 2023 Medium
- The value of \(\sin \left(\cot ^{-1} x\right)\) isMHT CET 2023 Easy
More PYQs from MHT CET
- Match the terms is Column-I with their explanation in Column-II:
Column I Column II A. Polycythemia I. Decrease in number of WBCs B. Erythrocytopenia II. Increase in number of RBCs C. Leukemia III. Decrease in number of RBCs D. Leucopenia IV. Uncontrolled increase in number of WBCs MHT CET 2021 Hard - Which among the following has the highest melting point?MHT CET 2024 Medium
- The diagonal of a square is changing at the rate of \(0.5 \mathrm{~cm} / \mathrm{sec}\). Then the rate of change of area when the area is \(400 \mathrm{~cm}^2\) is equal toMHT CET 2023 Medium
- What is the standard free energy change for the cell, having following cell reaction?
\(2 \mathrm{Ag}_{(\mathrm{aq} .)}^{+}+\mathrm{Cd}_{(\mathrm{s})} \longrightarrow 2 \mathrm{Ag}_{(\mathrm{s})}+\mathrm{Cd}_{(\mathrm{aq})}^{2+}, \mathrm{E}^{\circ} \mathrm{cell}\) \(=1 \cdot 20 \mathrm{~V}\)MHT CET 2020 Medium - A fair die with numbers 1 to 6 on their faces is thrown. Let \(\mathrm{X}\) denote the number of factors of the number, on the uppermost face, then the probability distribution of \(\mathrm{X}\) isMHT CET 2023 Easy
- Two wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced byMHT CET 2025 Medium