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

Similar Questions

Explore conceptually related problems

If |vec(a)| = sqrt(3), |vec(b)| = 2 and angle between vec(a) and vec(b) is 60^(@) , find vec(a).vec(b) .

If |vec a| =4 , |vec b | = 2 and angle between vec a and vec b is pi/6 , then (vec a xx vec b)^(2) is

Let the vectors a and b be such that |a|=3 and |b|=(sqrt(2))/(3) , then axxb is a unit vector, if the angle between a and b is

Three vertices of a parallelogram are (a + b ,a - b ) , (2a + b, 2a - b), and (a - b, a + b) . Find the 4th vertex.

If vec a + vec b + vec c = 0 and |vec a|= 3, |vec b| = 4 and |vec c| = sqrt37 , then the angle between vec a and vec b is

If sin (A+B)=1 and cos (A-B) = (sqrt(3))/(2) , find A and B.

In a DeltaABC , a=2b and |A-B|=(pi)/(3) . Then /_C is

Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B ( 2+ sqrt(3) , 5 ) and C (2, 6 ) .

Let the vectors vec a and vec b be such that |vec a| = 3 and |vec b| = sqrt2/3 , then vec a xx vec b is a unit vector, if the angle between vec a and vec b is