English
Hindi

Question

Download Solution PDF

What is the value of λ for which the vectors  are coplanar 

This question was previously asked in
Navik GD Mathematics 20 March 2021 (All Shifts) Questions
Download PDF Attempt in App
View all Indian Coast Guard Navik GD Papers >
  1. 5
  2. 4
  3. 2
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1
Free Tests
View all Free tests >
Free
CRPF Head Constable & ASI Steno (Final Revision): Mini Mock Test
40 Qs. 40 Marks 45 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

Condition for coplanarity:

​Calculation:

Here,  are coplanar

1(λ - 1) + 1(2λ + λ) + 1(-2 - λ) = 0

λ - 1 + 2λ + λ + -2 - λ = 0

3λ - 3 = 0

λ = 1

Hence, option (4) is correct.

Download Solution PDF
Latest Indian Coast Guard Navik GD Updates

Last updated on Jul 4, 2025

-> The Indian Coast Guard Navik GD Application Correction Window is open now. Candidates can make the changes in the Application Forms through the link provided on the official website of the Indian Navy.

-> A total of 260 vacancies have been released through the Coast Guard Enrolled Personnel Test (CGEPT) for the 01/2026 and 02/2026 batch.

-> Candidates can apply online from 11th to 25th June 2025.

-> Candidates who have completed their 10+2 with Maths and Physics are eligible for this post. 

-> Candidates must go through the Indian Coast Guard Navik GD previous year papers.

Exams Tests Super Practice

More Scalar and Vector Product Questions

Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let θ be the angle between two unit vectors \(\rm \vec a\ and\ \vec b. \ if\ \vec a+2\vec b\) is perpendicular to \(\rm 5\vec a-4\vec b\) then what is cos θ + cos 2θ equal to?
Q3.For what value of the angle between the vectors \(\rm \vec a\ and \ \vec b\) is the quantity \(\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|\) maximum? 
Q4.What is 3α + 2β equal to if (2î + 6ĵ + 27k̂) × (î + αĵ + βk̂) is a null vector?
Q5.Three vectors \(\vec{a}, \vec{b}\) and \(\vec{c}\) are such that \(|\vec{a}|=3,|\vec{b}|=4,|\vec{c}|=5\) and each of these is perpendicular to the sum of the other two. What is \(|\vec{a}+\vec{b}+\vec{c}|\) ?
Q6.If \(\vec{a}=2 \hat{i}+5 \hat{j}+3 \hat{k}\) , \(\vec{b}=3 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{c}=2 \hat{i}+7 \hat{j}+4 \hat{k}\), then \(|(\vec{a}-\vec{b}) \times(\vec{c}-\vec{a})|\) is
Q7.If \(\hat{a}\) and \(\hat{b}\) are unit vectors, and the angle between them is θ, then \(\sin \frac{\theta}{2}\) is
Q8.If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a} \times(\vec{b} \times \vec{c})=\frac{1}{2} \vec{b}\), then the angle which \(\vec{a}\) makes with \(\vec{c}\) is
Q9.Vector \(\rm \vec A\) and \(\rm \vec B\) are parallel, then:
Q10.If \(\vec{a}\) and \(\vec{b}\) are unit vectors and θ is angle between them, then \(\frac{|\vec{a}-\vec{b}|}{2}\) is:

More Vector Algebra Questions

Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let ABCDEF be a regular hexagon. If \(\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}\) then what is mn equal to 
Q3.Let θ be the angle between two unit vectors \(\rm \vec a\ and\ \vec b. \ if\ \vec a+2\vec b\) is perpendicular to \(\rm 5\vec a-4\vec b\) then what is cos θ + cos 2θ equal to?
Q4.For what value of the angle between the vectors \(\rm \vec a\ and \ \vec b\) is the quantity \(\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|\) maximum? 
Q5.What is 3α + 2β equal to if (2î + 6ĵ + 27k̂) × (î + αĵ + βk̂) is a null vector?
Q6.A vector \(\rm \vec{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}(\alpha, \beta \in {R}) \) lies in the plane of the vectors, \(\rm \vec{b}=\hat{i}+\hat{j}\) and \(\rm \vec{c}=\hat{i}-\hat{j}+4 \hat{k}\). If \(\rm \vec{a}\) bisects the angle between \(\rm \vec{b}\) and \(\rm \vec{c}\), then
Q7.The vector equation of the plane passing through the intersection of the planes \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1\) and \(\vec{r} \cdot(\hat{i}-2 \hat{j})=-2\) and the point (1, 0, 2) is:
Q8.Let ABC be a triangle such that \(\overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\vec{b}, \overrightarrow{A B}=\vec{c},|\vec{a}|=6 \sqrt{2},|\vec{b}|=2 \sqrt{3}\) and \(\vec{b} \cdot \vec{c}=12\) Consider the statements : \(\text { (S1): }|(\vec{a} \times \vec{b})+(\vec{c} \times \vec{b})|-|\vec{c}|=6(2 \sqrt{2}-1)\) \(\text { (S2): } \angle A C B=\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then
Q9.Let a unit vector which makes an angle of 60° with 2î + 2ĵ - k̂ and an angle of 45° with î - k̂ be \(\vec{C}\). Then \(\vec{C}+ \left(-\frac{1}{2}\hat{i} + \frac{1}{3\sqrt{2}}\hat{j} - \frac{\sqrt{2}}{3}\hat{k}\right)\) is:
Q10.If a̅, b̅, c̅, d̅ are the position vectors of the points A, B, C, D, respectively, such that no three of them are collinear and a̅ + c̅ = b̅ + d̅. then the quadrilateral ABCD is: 
Suggested Test Series
View All >
General Knowledge for All Defence Exams
317 Total Tests with 1 Free Tests
Start Free Test
ICG Navik GD (01/2026 - 02/2026) Mock Test Series
251 Total Tests with   1 Free Tests
Start Free Test

NDA Important Links

ResultAdmit CardApplication FormEligibilitySalarySyllabus

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti casino apk teen patti master update teen patti plus teen patti real cash withdrawal