If the vectors `hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j)` represent the diagonals of a parallelogram, then its area will be

Question

If the vectors `hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j)` represent the diagonals of a parallelogram, then its area will be

If the vectors `hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j)` represent the diagonals of a parallelogram, then its area will be
A. `sqrt(21)`
B. `sqrt(21)/2`
C. `2sqrt(21)`
D. `sqrt(21)/4`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

रेखा ` overset to r =(2hati +hat j -hat k )+lambda (2hat i +2hat j +hat k ) `और समतल ` oversetto r .(6hat i-3hat j +2hatk )+1=0` के बीच का कोण ज्ञात क

2 Answers 4 Views

If `a=hat(i)+hat(j)+hat(k), b=hat(i)+3hat(j)+5hat(k)` and `c=7hat(i)+9hat(j)+11 hat(k)`, then the area of the parallelogram having diagonals `a+b` and

2 Answers 5 Views

If `a=hat(i)+hat(j)+hat(k), b=2hat(i)+lambda hat(j)+hat(k), c=hat(i)-hat(j)+4hat(k)` and `a.(b xx c)=10`, then `lambda` is equal to

2 Answers 5 Views

If three vectors `2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k)` and `3hat(i)+lambda hat(j)+5hat(k)` are coplanar, then the value of `lambda` is

2 Answers 4 Views

The position vectors of vertices of a `Delta ABC` are `4hat(i)-2hat(j), hat(i)-3hat(k)` and `-hat(i)+5hat(j)+hat(k)` respectively, then `angle ABC` is

2 Answers 4 Views

Given `p=3hat(i)+2hat(j)+4hat(k), a=hat(i)+hat(j), b=hat(j)+hat(k), c=hat(i)+hat(k)` and `p=x a +y b +z c`, then x, y and z are respectively

2 Answers 4 Views

If the vectors `a=hat(i)+a hat(j)+a^(2) hat(k), b=hat(i)+b hat(j)+b^(2) hat(k)` and `c=hat(i)+chat(j)+c^(2) hat(k)` are three non-coplanar vectors and

2 Answers 5 Views

If vector `hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k)` and `2hat(i)+3hat(j)+lambda hat(k)` are coplanar, then `lambda` is equal to

2 Answers 5 Views

Area of rhombus is ......., where diagonals are `a=2hat(i)-3hat(j)+5hat(k)` and `b=-hat(i)+hat(j)+hat(k)`

2 Answers 5 Views

What vector must be added to the sum of two vectors `2hat(i)-hat(j)+3hat(k)and3hat(i)-2hat(j)-2hat(k).` So that the resultant is a unit vector alongZ-

2 Answers 8 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
Let `a=hati-3hatj+2hatk, b=-hati+2hatj`
Now, `axxb=|{:(hati,hatj,hatk),(1,-3,2),(-1,2,0):}|=-4hati-2hatj-hatk`
`:." "` Area of parallelogram `=1/2|axxb|=1/2sqrt(16+4+1)=sqrt(21)/2`

4 views Answered 2023-02-05 15:29