Prove that the four points 6 hat i-7 hat...

Prove that the four points `6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k` and `2 hat i+5 hat j+10 hatk` form a tetrahedron in space.

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Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

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If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are collinear, then

Find the value of lambda for which the three points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k are coplanar.

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

Find | -> axx -> b|, if -> a=2 hat i+ hat j+3 hat k and -> b=3 hat i+5 hat j-2 hat k .

If four points 2hat(i) + hat(j) + hat(k), hat(i) + hat(j) - hat(k), hat(j) - hat(k) and lamda hat(j) + hat(k) are coplanar then lamda =

Find the value of lambda if the volume of a tetrahedron whose vertices are with position vectors hat i-6 hat j+10 hat k ,- hat i-3 hat j+7 hat k ,5 hat i- hat j+lambda hat k and 7 hat i-4 hat j+7 hat k is 11 cubic unit.

The position vectors of the four angular points of a tetrahedron are A( hat j+2 hat k),B(3 hat i+ hat k), C(4 hat i+3 hat j+6 hat k)a n dD(2 hat i+3 hat j+2 hat k)dot Find the volume of the tetrahedron A B C Ddot

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions

If vec a , vec b and vec c are three non-zero vectors, no two of whic...
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Check whether the given three vectors are coplanar or non-coplanar. -2...
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Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ...
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Show, by vector methods, that the angularbisectors of a triangle are c...
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Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...
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Find the least positive integral value of x for which the angle betwee...
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If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k ...
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A vector has component A1, A2a n dA3 in a right -handed rectangular Ca...
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If two side of a triangle are hat i+2 hat j and hat i+ hat k , then...
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If in parallelogram ABCD, diagonal vectors are vec A C=2 hat i+3 ha...
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Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b...
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Check whether the three vectors 2 hat i+2 hat j+3 hat k ,-3 hat i+3...
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