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Find the area of the triangle whose adja...

Find the area of the triangle whose adjacent sides are determined by the vectors `vec(a)=(-2 hat(i)-5 hat(k)) and vec(b)= ( hat(i)- 2 hat(j) - hat(k))`.

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The correct Answer is:
`(1)/(2)(sqrt(65))` sq. units
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Find the area of the trinagle whose two adjacent sides are determined by the vectors (i) vec(a)= -2hat(i)-5 hat(k) and vec(b)=hat(i)- 2 hat(j)- hat(k) (ii) vec(a)= 3 hat(i)+ 4 hat(j) and vec(b)=-5hat(i)+7 hat(j).

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Find the area of the parallelogram whose adjacent sides are determined by the vectors vec a=hat i-hat j+3hat k and vec b=2hat i-hat 7hat j+hat k

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

Calculate the area of the parallelogram when adjacent sides are given by the vectors vec(A)=hat(i)+2hat(j)+3hat(k) and vec(B)=2hat(i)-3hat(j)+hat(k) .

Determine the area of the parallelogram whose adjacent sides are formed by the vectors vec A = hat i -3 hat j + hat k and vec B = hat i + hat j + hat k .

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Find the projection of vec(a) = 2 hat(i) - hat(j) + hat(k) on vec(b) = hat(i) - 2 hat(j) + hat(k) .

Find the area of the parallelogram whose diagonals are represented by the vectors vec(d)_(1)=(2 hat(i) - hat(j)+ hat(k)) and vec(d)_(2) = (3 hat(i) + 4 hat(j) - hat(k)).

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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise For Session 2
  1. Find | vec axx vec b| , if vec a= hat i-7 hat j+7 hat ka n d vec b=3 ...

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  2. Find the values of gamma and mu for which (2hati+6hatj+27hatk)xx(hati+...

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  3. If a=2hat(i)+3hat(j)-hat(k), b=-hat(i)+2hat(j)-4hat(k), c=hat(i)+hat(j...

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  4. Prove that ( vec adot hat i)( vec axx hat i)+( vec adotj)( vec axx hat...

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  5. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd then show that veca...

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  6. If ( vec axx vec b)^2+( vec adot vec b)^2=144a n d| vec a|=4, then fin...

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  7. If |a|=2,|b|=7 and vec ax vec b=3 hat i+2 hat j+6 hat k , find the...

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  8. Let the vectors vec aa n d vec b be such that | vec a|=3| vec b|=(sqr...

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  9. If |veca|=sqrt(26), |vecb|=7 and |vecaxxvecb|=35, find veca.vecb

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  10. Find a unit vector perpendicular to the plane of two vectors a=hat(i)-...

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  11. Find a vector of magnitude 15, which is perpendicular to both the vect...

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  12. Let -> a= hat i+4 hat j+2 hat k , -> b=3 hat i-2 hat j+7 hat k and...

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  13. Let A,B and C be the unit vectors . Suppose that A.B=A.C =0 and the a...

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  14. Find the area of the triangle whose adjacent sides are determined by t...

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  15. Find the area of parallelogram whose adjacent sides are represented by...

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  16. What is the area of the parallelogram having diagonals 3hat(i) + hat(j...

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  17. A force F=2hat(i)+hat(j)-hat(k) acts at point A whose position vector...

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  18. Find the moment of vec F about point (2, -1, 3), where force vec ...

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  19. Forces 2hat(i)+hat(j), 2hat(i)-3hat(j)+6hat(k) and hat(i)+2hat(j)-hat(...

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