Balbharti12th Maharashtra State Board Maths Solutions BookPdf Chapter 5 Vectors Ex 5.5 Questions and Answers.
Maharashtra State Board 12th Maths Solutions Chapter 5 Vectors Ex 5.5
Question 1
Maharashtra Board Solution
Find ∙( × ), if = , = and =
Solution & Step-by-Step Answer:
∙( × ) = = 3(9 + 2) + 1 (6 – 5) + 4(4 + 15) = 33 + 1 + 76 = 110.
Question 2
Maharashtra Board Solution
If the vectors and are to co-terminus edges of the parallelo piped, then find the volume of the parallelopiped.
Solution & Step-by-Step Answer:
= 3(8 + 3) – 0(16 + 9) + 5(4 – 6) = 33 – 0 – 10 = 23 ∴ volume of the parallelopiped = = 23 cubic units.
Question 3
Maharashtra Board Solution
If the vectors and are coplanar, then find the value of p.
Solution & Step-by-Step Answer:
∴ -3(0 + 2p) – 4(0 – 2) – 2(-p – 0) = 0 ∴ -6p + 8 + 2p = 0 ∴ -4p = -8 P = 2.
Question 4
Maharashtra Board Solution
Prove that : (i) {a} {b}+{c} {a}+{b}+{c} = 0
Solution & Step-by-Step Answer:
(ii) ( – – )∙[( – ) × – – ] = 3[ – – ]
Question is modified.
( – – ) [( – ) × – – ] = 3[ ]
Solution:
Question 5
Maharashtra Board Solution
If =3 – 2 prove that [ ] = 0
Solution & Step-by-Step Answer:
We use the results : × = 0 and if in a scalar triple product, two vectors are equal, then the scalar triple product is zero.
Question 6
Maharashtra Board Solution
If u = , = and = are given vectors, then find (i) [ + ]∙[( × ) × ( × )] Question is modified. If = , = and = are given vectors, then find [ + ]∙[( × ) × ( × )]
Solution & Step-by-Step Answer:
= 1(6 – 18) + 1 (-6 + 6) + 0 = -12 + 0 + 0 = -12.
Question 7
Maharashtra Board Solution
Find the volume of a tetrahedron whose vertices are A( -1, 2, 3) B(3, -2, 1), C (2, 1, 3) and D(-1, -2, 4).
Solution & Step-by-Step Answer:
The position vectors , , and of the points A, B, C and D w.r.t. the origin are = , = , = and
Question 8
Maharashtra Board Solution
If = , = and =, then verify that × ( × ) = ( ⋅ ) – ( ⋅ )
Solution & Step-by-Step Answer:
From (1) and (2), we get × ( × ) = ( ⋅ ) – ( ⋅ )
Question 9
Maharashtra Board Solution
If, = , = and = then find (i) × ( × )
Solution & Step-by-Step Answer:
(ii) ( × ) × Are the results same? Justify.
Solution:
× ( × ) ≠ ( × ) ×
Question 10
Maharashtra Board Solution
Show that × ( × ) + × ( × ) + × ( × ) = 0
Solution & Step-by-Step Answer:
