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Compute bar(a) xx (bar(b) + bar(c )) + b...

Compute `bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + bar(c ) xx (bar(a)+bar(b))`

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`vec(0)`
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Compute 2 bar(j) xx (3bar(i) - 4bar(k)) + (bar(i)+2bar(j)) xx bar(k) .

Find the perpendicular distance of the point bar(c ) from the straight line bar(r )= bar(a) + t bar(b) and hence deduce that the area of the triangle whose vertices are the points bar(a), bar(b) and bar(c )" is" (1)/(2)|bar(b) xx bar(c ) + bar( c) xx bar(a) + bar(a) xx bar(b)| .

If bar(a)bar(b)bar(c ) and bar(d) are vectors such that bar(a) xx bar(b) = bar(c ) xx bar(d) and bar(a) xx bar(c ) = bar(b)xxbar(d) . Then show that the vectors bar(a) - bar(d) and bar(b) -bar(c ) are parallel.

If bar(a)= 2bar(i) - 3bar(j) + 5bar(k), bar(b)= - bar(i) + 4bar(j)+ 2bar(k) then find (bar(a) + bar(b)) xx (bar(a) - bar(b)) and unit vector perpendicular to both bar(a) + bar(b) " & " bar(a)- bar(b) .

bar(a), bar(b), bar(c) are non-coplanar vectors. Prove thate the following four points are coplanar - bar(a) + 4 bar(b) - 3 bar(c) , 3 bar(a) + 2 bar(b) - 5 bar(c) - 3 bar(a) + 8 bar(b) - 5 bar(c) , - 3 bar(a) + 2 bar(b) + bar(c)

bar(a) , bar(b), bar (c ) , are non-coplanar vectors, Prove that the following four points are coplanar. 6bar(a) + 2bar(b) - bar(c ), 2bar(a) - bar(b) + 3bar(c ), -bar(a) + 2bar(b)-4bar(c ), -12bar(a)-bar(b)-3bar(c ) .

AAKASH SERIES-VECTOR (CROSS) PRODUCT OF TWO VECTORS-Exercise-3.1 (very Short Answer Questions)
  1. If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) ...

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  2. If |bar(a)|=2, |bar(b)|=3, (bar(a), bar(b))= pi//6, then find (bar(a) ...

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  3. If |bar(a) xx bar(b)|= bar(a).bar(b), then find the angle between the ...

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  4. If theta is the angle between the vectors bar(i) + bar(j) , bar(j) + b...

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  5. If 4bar(i) + (2p)/3 bar(j)+ pbar(k) is parallel to the vector bar(i) ...

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  6. If bar(p) = xbar(i) + ybar(j) + zbar(k), find the value of |bar(p) xx ...

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  7. For any vector bar(a) show that |bar(a) xx bar(i)|^(2) + |bar(a) xx ba...

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  8. Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + b...

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  9. Compute 2 bar(j) xx (3bar(i) - 4bar(k)) + (bar(i)+2bar(j)) xx bar(k).

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  10. If |bar(a)| = 13, |bar(b)| = 5, and bar(a).bar(b) = 60, then find |bar...

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  11. If bar(a) = bar(i) + 2bar(j) + 3bar(k), bar(b) = 3bar(i) +5bar(j) -bar...

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  12. Find the area of the triangle having (3bar(i)+4bar(j)),(-5bar(i)+7bar(...

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  13. The area of the triangle with vertices (1,2,3), (2,5,-1), (-1,1,2) is

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  14. Find the area of the parallelogram whose adjacent sides are bar(a) = 2...

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  15. Find the vector area and area of the parallelogram having bar(a) = bar...

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  16. Find the area of the parallelogram whose diagonals are 3bar(i) + bar(j...

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