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Evaluate the following :
Find the volume of the parallelepiped whose coterminous edges are represented by the vectors:
Show that each of the following triads of vectors is coplanar :
Find the value of λ so that the following vectors are coplanar.
Show that the four points having position vectors are not coplanar.
Show that the points A( – 1, 4, – 3), B(3, 2, – 5), C( – 3, 8, – 5) and D( – 3, 2, 1) are coplanar.
Show that four points whose position vectors are are coplanar.
Find the value of for which the four points with position vectors and are coplanar.
Prove that : -
and are the position vectors of points A, B and C respectively, prove that : is a vector perpendicular to the plane of triangle ABC.
Let and Then,
If and find which makes and coplanar.
If and show that no value of can make and coplanar.
Find for which the points A(3, 2, 1), B(4, λ, 5), C(4, 2, – 2) and D(6, 5, – 1) are coplanar.
If four points A, B, C and D with position vectors and respectively are coplanar, then find the value of x.
Write the value of
Find the values of ‘a’ for which the vectors and are coplanar.
Find the volume of the parallelepiped with its edges represented by the vectors
If are non-collinear vectors, then find the value of
If the vectors (sec2 A) are coplanar, then find the value of cosec2A A + cosec2B + cosec2C.
For any two vectors of of magnitudes 3 and 4 respectively, write the value of
If then find the value of λ + μ.
If are non-coplanar vectors, then find the value of
Find , if and
Mark the correct alternative in each of the following:
If lies in the plane of vectors and , then which of the following is correct?
The value of , where ,, is
If , , are three non-coplanar mutually perpendicular unit vectors, then is
If for some non-zero vector , then the value of , is
For any three vector the expression equals
If , , are non-coplanar vectors, then is
Let and be three non-zero vectors such that c⃗ is a unit vector perpendicular to both a⃗ and b⃗ . If the angle between a⃗ and b⃗ is, then is equal to
If and then the volume of the parallelepiped with conterminous edges , , is
If the vectors and are coplanar, then m =
For non-zero vectors a⃗, b⃗ and c⃗ the relation holds good, if
If a⃗ ,b⃗,c⃗ are three non-coplanar vectors, then equal.
is equal to