HARD
12th CBSE
IMPORTANT
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The area of the triangle with vertices, A(2,3,5), B(3,5,8) and C(2,7,8) is k2 square units.

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Important Questions on Vector or Cross Product

HARD
12th CBSE
IMPORTANT
If a=2i^-3j^+k^,b=-i^+k^,c=2j^-k^ are three vectors, if the area of the parallelogram isk2 sq. units having diagonals a+b and b+c then find the value of k.
HARD
12th CBSE
IMPORTANT
The two adjacent sides of a parallelogram are 2i^-4j^+5k^ and i^-2j^-3k^. Find the unit vector parallel to one of its diagonals. If its area is 11k square units. Then the value of k is
MEDIUM
12th CBSE
IMPORTANT
If either a=0 or b=0, then a×b=0. Is the converse true? Justify your answer with an example.
HARD
12th CBSE
IMPORTANT
If a=a1i^+a2j^+a3k^,b=b1i^+b2j^+b3k^ and c=c1i^+c2j^+c3k^, then verify that a×(b+c)=a×b+a×c
HARD
12th CBSE
IMPORTANT

If the area of the triangle with vertices: A(1,1,2), B(2,3,5) and C(1,5,5) is k2 square units. Find the value of k.

HARD
12th CBSE
IMPORTANT

The area of the triangle with vertices: A(1,2,3), B(2,-1,4) and C(4,5,-1) is k2. Find the value of k.

MEDIUM
12th CBSE
IMPORTANT

Find all vectors of magnitude 103 that are perpendicular to the plane of i^+2j^+k^ and -i^+3j^+4k^.

HARD
12th CBSE
IMPORTANT
The two adjacent sides of a parallelogram are 2i^-4j^-5k^ and 2i^+2j^+3k^. Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.