Home
Class 12
MATHS
The length of longer diagonal of the p...

The length of longer diagonal of the parallelogram constructed on `5a + 2b` and `a-3b` . If it is given that `|a| = 2sqrt(2),|b|` = 3 and angle between a and b is `(pi)/(4)` is

A

15

B

`sqrt(113)`

C

`sqrt(593)`

D

`sqrt(369)`

Text Solution

Verified by Experts

The correct Answer is:
C
Length of the two diagonasl will be
`d_(1)=|(5a+2b)+(a-3b)|`
and `d_(2)=|(5a+2b)-(a-3b)|`
`impliesd_(1)=|6a-b|,d_(2)=|4a+5b|`
thus, `d_(1)=sqrt(|6a|^(2)+|-b|^(2)+2|6a||-b|cos(pi-pi//4))`
`=sqrt(36(2sqrt(2))^(2)+9+12*2sqrt(2)*3*(-(1)/(sqrt(2))))=15`
`d_(2)=sqrt(|4a|^(2)+|5b|^(2)+2|4a||5b|"cos"(pi)/(4))`
`=sqrt(16xx8+25xx9+40xx2sqrt(2)xx3xx(1)/(sqrt(2)))`
`=sqrt(593)`
`therefore` Length of the longer diagonal`=sqrt(593)`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

The length of the longer diagonal of the parallelogram constructed on 5vec a+2vec b and vec a-3vec b if it is given that |vec a|=2sqrt(2),|vec b|=3 and angle between vec a and vec b is pi/4 is 15 b.sqrt(113) c.sqrt(593) d.sqrt(369)

The length of the longer diagonal of the parallelogram constructed on 5veca + 2vecb and veca - 3vecb, if it is given that |veca|=2sqrt2, |vecb|=3 and veca. Vecb= pi/4 is

The length of longer diagonal of the parallelogram constructed an 5bar(a)+2bar(b) and bar(a)-3bar(b) as sides if it is given |bar(a)|=2sqrt(2) , |bar(b)|=3 and (bar(a),bar(b))=pi/4 is

The ratio of lengths of diagonals of the parallelogram constructed on the vectors vec(a)=3vec(p)-vec(q),vec(b)=vec(p)+3vec(q) is (given that |vec(p)|=|vec(q)|=2 and angle between vec(p) and vec(q) is pi//3 ).

Consider a parallelogram constructed as 5bara+2barb and bara-3barb where |a|=2sqrt2 and |b|=3 the angle between bara and barb is pi//4 then the length of the longer diagonal is

If a and b are the two vectors such that |a|-3sqrt(3),|b|=4 and |a+b|=sqrt(7) , then the angle between a and b is