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x
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| if
Solution :
We have,
Solution :
We have
and an acute angle θ with
then find θ and hence, the components of
Solution :
Question 5. Find λ and μ if
Solution :
Question
6. Given that
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be given as
then show that
Solution :
We have
,
Hence, the given result is proved.
Question
8. It either
Hence, the converse of the given statement need not be true.
Question
9. Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).
Solution :
The vertices of triangle ABC are given as A (1, 1, 2), B (2, 3, 5), and
C (1, 5, 5).
The adjacent sides
and
of ΔABC are given as:
Hence, the area of ΔABC is √61/2 sq. units.
Question
10. Find the area of the parallelogram whose adjacent sides are determined by the vectors
Solution :
The area of the parallelogram whose adjacent sides are
Hence, the area of the given parallelogram is 15√2 sq. units.
Question
11. Let the vectors
Therefore, option (B) is correct.
Question
12. Area of a rectangle having vertices A, B, C and D with position vectors
respectively is:
(A) 1/2
(B) 1
(C) 2
(D) 4
Solution :
The position vectors of vertices A, B, C, and D of rectangle ABCD are given as:
The adjacent sides
Now, it is known that the area of a parallelogram whose adjacent sides are
