5830 Views

The angles which a unit vector I+ j+ sqaure root 2k makes with X Y & Z respectively are a).60 , 60 , 60 b). 45 , 45 ,45 c). 60 , 60 , 45 d). 45 ,45 , 60


nafeesahmad0616 10th Jan, 2021
Answer (1)
ARYAN SAGAR 10th Jan, 2021
Dear student,

Let the angle made by X axis be alpha
Let the angle made by Y axis be beta
Let the angle made by Z axis be gamma

Let the vector be A vector = i + j + ((2)^1/2)k

Now |A vector| = {1^2 + 1^2 + ((2)^1/2)^2}^1/2

And therefore magnitude of A vector = (4)^1/2 =2

Therefore unit vector A = i/2 + j/2 + {(2)^1/2k}/2

And therefore angle with X axis :-
cos( alpha ) = 1/2
So, alpha = 60 degrees

Therefore angle with Y axis :-
cos ( beta ) = 1/2
So, beta = 60 degrees

Therefore angle with Z axis :-
cos ( gamma ) = 1/(2)^1/2
So, gamma = 45 degrees.

So, the angle is ( 60, 60, 45 ).

This, option C is correct.

Related Questions

Amity University, Noida Law A...
Apply
700+ Campus placements at top national and global law firms, corporates, and judiciaries
UPES Integrated LLB Admission...
Apply
Ranked #28 amongst Institutions in India by NIRF | Ranked #1 in India for Academic Reputation by QS University Rankings | 16.6 LPA Highest CTC
Great Lakes PGPM & PGDM 2025
Apply
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Extended Application Deadline: 10th Jan 2024
ISBR Business School PGDM Adm...
Apply
250+ Companies | Highest CTC 16 LPA | Average CTC 8 LPA | Ranked as Platinum Institute by AICTE for 6 years in a row | Awarded Best Business School...
Chandigarh University Admissi...
Apply
Ranked #1 Among all Private Indian Universities in QS Asia Rankings 2025 | Scholarships worth 210 CR
Manav Rachna University Law A...
Apply
Admissions open for B.A. LL.B. (Hons.), B.B.A. LL.B. (Hons.) and LL.B Program (3 Years)
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books