Chapter 5 Vectors Ex 5.5

Question 1.

Question 2.

Solution:

= 3(8 + 3) – 0(16 + 9) + 5(4 – 6)
= 33 – 0 – 10 = 23

= 23 cubic units.

Question 3.

Solution:

∴ -3(0 + 2p) – 4(0 – 2) – 2(-p – 0) = 0
∴ -6p + 8 + 2p = 0
∴ -4p = -8
P = 2.

Question 4.
Prove that :
(i) [latex]\bar{a} \bar{b}+\bar{c} \bar{a}+\bar{b}+\bar{c}[/latex] = 0
Solution:

Solution:

Question 5.

Question 6.

Solution:

= 1(6 – 18) + 1 (-6 + 6) + 0
= -12 + 0 + 0 = -12.

Question 7.
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:

Question 8.

Solution:

Solution:

a¯ × (b¯ × c¯) ≠ (a¯ × b¯) × c¯

Question 10.

Solution: